Question: Which magnification is less important for visual telescopes or binoculars?

Answer: Linear

<hl> Linear magnification M is not always the most useful measure of magnifying power. <hl> For instance, when characterizing a visual telescope or binoculars that produce only a virtual image, one would be more concerned with the angular magnification—which expresses how much larger a distant object appears through the telescope compared to the naked eye. In the case of a camera one would quote the plate scale, which compares the apparent (angular) size of a distant object to the size of the real image produced at the focus. The plate scale is the reciprocal of the focal length of the camera lens; lenses are categorized as long-focus lenses or wide-angle lenses according to their focal lengths.

<hl> Linear <hl> magnification M is not always the most useful measure of magnifying power. For instance, when characterizing a visual telescope or binoculars that produce only a virtual image, one would be more concerned with the angular magnification—which expresses how much larger a distant object appears through the telescope compared to the naked eye. In the case of a camera one would quote the plate scale, which compares the apparent (angular) size of a distant object to the size of the real image produced at the focus. The plate scale is the reciprocal of the focal length of the camera lens; lenses are categorized as long-focus lenses or wide-angle lenses according to their focal lengths.


Question: If the angular magnification is 5, then how much larger does an object appear to the eye without the lens?

Using an inappropriate measurement of magnification can be formally correct but yield a meaningless number. For instance, using a magnifying glass of 5 cm focal length, held 20 cm from the eye and 5 cm from the object, produces a virtual image at infinity of infinite linear size: M = ∞. But the angular magnification is 5, meaning that the object appears 5 times larger to the eye than without the lens. When taking a picture of the moon using a camera with a 50 mm lens, one is not concerned with the linear magnification M ≈ −50 mm / 380000 km = −1.3×10−10. Rather, the plate scale of the camera is about 1°/mm, from which one can conclude that the 0.5 mm image on the film corresponds to an angular size of the moon seen from earth of about 0.5°.

Answer: 5 times

Using an inappropriate measurement of magnification can be formally correct but yield a meaningless number. <hl> For instance, using a magnifying glass of 5 cm focal length, held 20 cm from the eye and 5 cm from the object, produces a virtual image at infinity of infinite linear size: M = ∞. But the angular magnification is 5, meaning that the object appears 5 times larger to the eye than without the lens. <hl> When taking a picture of the moon using a camera with a 50 mm lens, one is not concerned with the linear magnification M ≈ −50 mm / 380000 km = −1.3×10−10. Rather, the plate scale of the camera is about 1°/mm, from which one can conclude that the 0.5 mm image on the film corresponds to an angular size of the moon seen from earth of about 0.5°.

Using an inappropriate measurement of magnification can be formally correct but yield a meaningless number. For instance, using a magnifying glass of 5 cm focal length, held 20 cm from the eye and 5 cm from the object, produces a virtual image at infinity of infinite linear size: M = ∞. But the angular magnification is 5, meaning that the object appears <hl> 5 times <hl> larger to the eye than without the lens. When taking a picture of the moon using a camera with a 50 mm lens, one is not concerned with the linear magnification M ≈ −50 mm / 380000 km = −1.3×10−10. Rather, the plate scale of the camera is about 1°/mm, from which one can conclude that the 0.5 mm image on the film corresponds to an angular size of the moon seen from earth of about 0.5°.


Question: What magnification type is unimportant when shooting a picture of the moon with a 50 mm lens?

Answer: linear magnification

Using an inappropriate measurement of magnification can be formally correct but yield a meaningless number. For instance, using a magnifying glass of 5 cm focal length, held 20 cm from the eye and 5 cm from the object, produces a virtual image at infinity of infinite linear size: M = ∞. But the angular magnification is 5, meaning that the object appears 5 times larger to the eye than without the lens. <hl> When taking a picture of the moon using a camera with a 50 mm lens, one is not concerned with the linear magnification M ≈ −50 mm / 380000 km = −1.3×10−10. <hl> Rather, the plate scale of the camera is about 1°/mm, from which one can conclude that the 0.5 mm image on the film corresponds to an angular size of the moon seen from earth of about 0.5°.

Using an inappropriate measurement of magnification can be formally correct but yield a meaningless number. For instance, using a magnifying glass of 5 cm focal length, held 20 cm from the eye and 5 cm from the object, produces a virtual image at infinity of infinite linear size: M = ∞. But the angular magnification is 5, meaning that the object appears 5 times larger to the eye than without the lens. When taking a picture of the moon using a camera with a 50 mm lens, one is not concerned with the <hl> linear magnification <hl> M ≈ −50 mm / 380000 km = −1.3×10−10. Rather, the plate scale of the camera is about 1°/mm, from which one can conclude that the 0.5 mm image on the film corresponds to an angular size of the moon seen from earth of about 0.5°.


Question: Using inappropriate measurements can technically be correct but yield a number that is what?

Answer: meaningless

<hl> Using an inappropriate measurement of magnification can be formally correct but yield a meaningless number. <hl> For instance, using a magnifying glass of 5 cm focal length, held 20 cm from the eye and 5 cm from the object, produces a virtual image at infinity of infinite linear size: M = ∞. But the angular magnification is 5, meaning that the object appears 5 times larger to the eye than without the lens. When taking a picture of the moon using a camera with a 50 mm lens, one is not concerned with the linear magnification M ≈ −50 mm / 380000 km = −1.3×10−10. Rather, the plate scale of the camera is about 1°/mm, from which one can conclude that the 0.5 mm image on the film corresponds to an angular size of the moon seen from earth of about 0.5°.

Using an inappropriate measurement of magnification can be formally correct but yield a <hl> meaningless <hl> number. For instance, using a magnifying glass of 5 cm focal length, held 20 cm from the eye and 5 cm from the object, produces a virtual image at infinity of infinite linear size: M = ∞. But the angular magnification is 5, meaning that the object appears 5 times larger to the eye than without the lens. When taking a picture of the moon using a camera with a 50 mm lens, one is not concerned with the linear magnification M ≈ −50 mm / 380000 km = −1.3×10−10. Rather, the plate scale of the camera is about 1°/mm, from which one can conclude that the 0.5 mm image on the film corresponds to an angular size of the moon seen from earth of about 0.5°.


Question: What is the focal length of a magnifying glass that's held 20 cm from the eye and 5 cm from the object yields an image of infinite linear size?

Answer: 5 cm

Using an inappropriate measurement of magnification can be formally correct but yield a meaningless number. <hl> For instance, using a magnifying glass of 5 cm focal length, held 20 cm from the eye and 5 cm from the object, produces a virtual image at infinity of infinite linear size: M = ∞. <hl> But the angular magnification is 5, meaning that the object appears 5 times larger to the eye than without the lens. When taking a picture of the moon using a camera with a 50 mm lens, one is not concerned with the linear magnification M ≈ −50 mm / 380000 km = −1.3×10−10. Rather, the plate scale of the camera is about 1°/mm, from which one can conclude that the 0.5 mm image on the film corresponds to an angular size of the moon seen from earth of about 0.5°.

Using an inappropriate measurement of magnification can be formally correct but yield a meaningless number. For instance, using a magnifying glass of <hl> 5 cm <hl> focal length, held 20 cm from the eye and 5 cm from the object, produces a virtual image at infinity of infinite linear size: M = ∞. But the angular magnification is 5, meaning that the object appears 5 times larger to the eye than without the lens. When taking a picture of the moon using a camera with a 50 mm lens, one is not concerned with the linear magnification M ≈ −50 mm / 380000 km = −1.3×10−10. Rather, the plate scale of the camera is about 1°/mm, from which one can conclude that the 0.5 mm image on the film corresponds to an angular size of the moon seen from earth of about 0.5°.


Question: What effect occurs because glass lens are shaped into spherical surfaces?

Spherical aberration occurs because spherical surfaces are not the ideal shape for a lens, but are by far the simplest shape to which glass can be ground and polished, and so are often used. Spherical aberration causes beams parallel to, but distant from, the lens axis to be focused in a slightly different place than beams close to the axis. This manifests itself as a blurring of the image. Lenses in which closer-to-ideal, non-spherical surfaces are used are called aspheric lenses. These were formerly complex to make and often extremely expensive, but advances in technology have greatly reduced the manufacturing cost for such lenses. Spherical aberration can be minimised by carefully choosing the surface curvatures for a particular application. For instance, a plano-convex lens, which is used to focus a collimated beam, produces a sharper focal spot when used with the convex side towards the beam source.

Answer: Spherical aberration

<hl> Spherical aberration occurs because spherical surfaces are not the ideal shape for a lens, but are by far the simplest shape to which glass can be ground and polished, and so are often used. <hl> Spherical aberration causes beams parallel to, but distant from, the lens axis to be focused in a slightly different place than beams close to the axis. This manifests itself as a blurring of the image. Lenses in which closer-to-ideal, non-spherical surfaces are used are called aspheric lenses. These were formerly complex to make and often extremely expensive, but advances in technology have greatly reduced the manufacturing cost for such lenses. Spherical aberration can be minimised by carefully choosing the surface curvatures for a particular application. For instance, a plano-convex lens, which is used to focus a collimated beam, produces a sharper focal spot when used with the convex side towards the beam source.

<hl> Spherical aberration <hl> occurs because spherical surfaces are not the ideal shape for a lens, but are by far the simplest shape to which glass can be ground and polished, and so are often used. Spherical aberration causes beams parallel to, but distant from, the lens axis to be focused in a slightly different place than beams close to the axis. This manifests itself as a blurring of the image. Lenses in which closer-to-ideal, non-spherical surfaces are used are called aspheric lenses. These were formerly complex to make and often extremely expensive, but advances in technology have greatly reduced the manufacturing cost for such lenses. Spherical aberration can be minimised by carefully choosing the surface curvatures for a particular application. For instance, a plano-convex lens, which is used to focus a collimated beam, produces a sharper focal spot when used with the convex side towards the beam source.


Question: What does spherical aberration cause in an image?

Answer: blurring

Spherical aberration occurs because spherical surfaces are not the ideal shape for a lens, but are by far the simplest shape to which glass can be ground and polished, and so are often used. Spherical aberration causes beams parallel to, but distant from, the lens axis to be focused in a slightly different place than beams close to the axis. <hl> This manifests itself as a blurring of the image. <hl> Lenses in which closer-to-ideal, non-spherical surfaces are used are called aspheric lenses. These were formerly complex to make and often extremely expensive, but advances in technology have greatly reduced the manufacturing cost for such lenses. Spherical aberration can be minimised by carefully choosing the surface curvatures for a particular application. For instance, a plano-convex lens, which is used to focus a collimated beam, produces a sharper focal spot when used with the convex side towards the beam source.

Spherical aberration occurs because spherical surfaces are not the ideal shape for a lens, but are by far the simplest shape to which glass can be ground and polished, and so are often used. Spherical aberration causes beams parallel to, but distant from, the lens axis to be focused in a slightly different place than beams close to the axis. This manifests itself as a <hl> blurring <hl> of the image. Lenses in which closer-to-ideal, non-spherical surfaces are used are called aspheric lenses. These were formerly complex to make and often extremely expensive, but advances in technology have greatly reduced the manufacturing cost for such lenses. Spherical aberration can be minimised by carefully choosing the surface curvatures for a particular application. For instance, a plano-convex lens, which is used to focus a collimated beam, produces a sharper focal spot when used with the convex side towards the beam source.


Question: What is the simplest shape glass can be ground and polished into?

Answer: spherical surfaces

<hl> Spherical aberration occurs because spherical surfaces are not the ideal shape for a lens, but are by far the simplest shape to which glass can be ground and polished, and so are often used. <hl> Spherical aberration causes beams parallel to, but distant from, the lens axis to be focused in a slightly different place than beams close to the axis. This manifests itself as a blurring of the image. Lenses in which closer-to-ideal, non-spherical surfaces are used are called aspheric lenses. These were formerly complex to make and often extremely expensive, but advances in technology have greatly reduced the manufacturing cost for such lenses. Spherical aberration can be minimised by carefully choosing the surface curvatures for a particular application. For instance, a plano-convex lens, which is used to focus a collimated beam, produces a sharper focal spot when used with the convex side towards the beam source.

Spherical aberration occurs because <hl> spherical surfaces <hl> are not the ideal shape for a lens, but are by far the simplest shape to which glass can be ground and polished, and so are often used. Spherical aberration causes beams parallel to, but distant from, the lens axis to be focused in a slightly different place than beams close to the axis. This manifests itself as a blurring of the image. Lenses in which closer-to-ideal, non-spherical surfaces are used are called aspheric lenses. These were formerly complex to make and often extremely expensive, but advances in technology have greatly reduced the manufacturing cost for such lenses. Spherical aberration can be minimised by carefully choosing the surface curvatures for a particular application. For instance, a plano-convex lens, which is used to focus a collimated beam, produces a sharper focal spot when used with the convex side towards the beam source.


Question: Non-sphereical lenses are called what?

Answer: aspheric lenses

Spherical aberration occurs because spherical surfaces are not the ideal shape for a lens, but are by far the simplest shape to which glass can be ground and polished, and so are often used. Spherical aberration causes beams parallel to, but distant from, the lens axis to be focused in a slightly different place than beams close to the axis. This manifests itself as a blurring of the image. <hl> Lenses in which closer-to-ideal, non-spherical surfaces are used are called aspheric lenses . <hl> These were formerly complex to make and often extremely expensive, but advances in technology have greatly reduced the manufacturing cost for such lenses. Spherical aberration can be minimised by carefully choosing the surface curvatures for a particular application. For instance, a plano-convex lens, which is used to focus a collimated beam, produces a sharper focal spot when used with the convex side towards the beam source.

Spherical aberration occurs because spherical surfaces are not the ideal shape for a lens, but are by far the simplest shape to which glass can be ground and polished, and so are often used. Spherical aberration causes beams parallel to, but distant from, the lens axis to be focused in a slightly different place than beams close to the axis. This manifests itself as a blurring of the image. Lenses in which closer-to-ideal, non-spherical surfaces are used are called <hl> aspheric lenses <hl>. These were formerly complex to make and often extremely expensive, but advances in technology have greatly reduced the manufacturing cost for such lenses. Spherical aberration can be minimised by carefully choosing the surface curvatures for a particular application. For instance, a plano-convex lens, which is used to focus a collimated beam, produces a sharper focal spot when used with the convex side towards the beam source.

Lenses in which closer-to-ideal, non-spherical surfaces are used are called <hl> aspheric lenses <hl> .


Question: What kind of lens is used to foucs a collimated beam which produces a much sharper focal spot?

Answer: plano-convex lens

Spherical aberration occurs because spherical surfaces are not the ideal shape for a lens, but are by far the simplest shape to which glass can be ground and polished, and so are often used. Spherical aberration causes beams parallel to, but distant from, the lens axis to be focused in a slightly different place than beams close to the axis. This manifests itself as a blurring of the image. Lenses in which closer-to-ideal, non-spherical surfaces are used are called aspheric lenses. These were formerly complex to make and often extremely expensive, but advances in technology have greatly reduced the manufacturing cost for such lenses. Spherical aberration can be minimised by carefully choosing the surface curvatures for a particular application. <hl> For instance, a plano-convex lens , which is used to focus a collimated beam, produces a sharper focal spot when used with the convex side towards the beam source. <hl>

Spherical aberration occurs because spherical surfaces are not the ideal shape for a lens, but are by far the simplest shape to which glass can be ground and polished, and so are often used. Spherical aberration causes beams parallel to, but distant from, the lens axis to be focused in a slightly different place than beams close to the axis. This manifests itself as a blurring of the image. Lenses in which closer-to-ideal, non-spherical surfaces are used are called aspheric lenses. These were formerly complex to make and often extremely expensive, but advances in technology have greatly reduced the manufacturing cost for such lenses. Spherical aberration can be minimised by carefully choosing the surface curvatures for a particular application. For instance, a <hl> plano-convex lens <hl>, which is used to focus a collimated beam, produces a sharper focal spot when used with the convex side towards the beam source.

For instance, a <hl> plano-convex lens <hl> , which is used to focus a collimated beam, produces a sharper focal spot when used with the convex side towards the beam source.


Question: Comatic aberration can also be referred to as what?

Coma, or comatic aberration, derives its name from the comet-like appearance of the aberrated image. Coma occurs when an object off the optical axis of the lens is imaged, where rays pass through the lens at an angle to the axis θ. Rays that pass through the centre of a lens of focal length f are focused at a point with distance f tan θ from the axis. Rays passing through the outer margins of the lens are focused at different points, either further from the axis (positive coma) or closer to the axis (negative coma). In general, a bundle of parallel rays passing through the lens at a fixed distance from the centre of the lens are focused to a ring-shaped image in the focal plane, known as a comatic circle. The sum of all these circles results in a V-shaped or comet-like flare. As with spherical aberration, coma can be minimised (and in some cases eliminated) by choosing the curvature of the two lens surfaces to match the application. Lenses in which both spherical aberration and coma are minimised are called bestform lenses.

Answer: Coma

<hl> Coma , or comatic aberration, derives its name from the comet-like appearance of the aberrated image. <hl> Coma occurs when an object off the optical axis of the lens is imaged, where rays pass through the lens at an angle to the axis θ. Rays that pass through the centre of a lens of focal length f are focused at a point with distance f tan θ from the axis. Rays passing through the outer margins of the lens are focused at different points, either further from the axis (positive coma) or closer to the axis (negative coma). In general, a bundle of parallel rays passing through the lens at a fixed distance from the centre of the lens are focused to a ring-shaped image in the focal plane, known as a comatic circle. The sum of all these circles results in a V-shaped or comet-like flare. As with spherical aberration, coma can be minimised (and in some cases eliminated) by choosing the curvature of the two lens surfaces to match the application. Lenses in which both spherical aberration and coma are minimised are called bestform lenses.

<hl> Coma <hl>, or comatic aberration, derives its name from the comet-like appearance of the aberrated image. Coma occurs when an object off the optical axis of the lens is imaged, where rays pass through the lens at an angle to the axis θ. Rays that pass through the centre of a lens of focal length f are focused at a point with distance f tan θ from the axis. Rays passing through the outer margins of the lens are focused at different points, either further from the axis (positive coma) or closer to the axis (negative coma). In general, a bundle of parallel rays passing through the lens at a fixed distance from the centre of the lens are focused to a ring-shaped image in the focal plane, known as a comatic circle. The sum of all these circles results in a V-shaped or comet-like flare. As with spherical aberration, coma can be minimised (and in some cases eliminated) by choosing the curvature of the two lens surfaces to match the application. Lenses in which both spherical aberration and coma are minimised are called bestform lenses.

<hl> Coma <hl> , or comatic aberration, derives its name from the comet-like appearance of the aberrated image.


Question: What is the ring-shaped image on the focal plane created by parallel rays called?

Answer: comatic circle

Coma, or comatic aberration, derives its name from the comet-like appearance of the aberrated image. Coma occurs when an object off the optical axis of the lens is imaged, where rays pass through the lens at an angle to the axis θ. Rays that pass through the centre of a lens of focal length f are focused at a point with distance f tan θ from the axis. Rays passing through the outer margins of the lens are focused at different points, either further from the axis (positive coma) or closer to the axis (negative coma). <hl> In general, a bundle of parallel rays passing through the lens at a fixed distance from the centre of the lens are focused to a ring-shaped image in the focal plane, known as a comatic circle . <hl> The sum of all these circles results in a V-shaped or comet-like flare. As with spherical aberration, coma can be minimised (and in some cases eliminated) by choosing the curvature of the two lens surfaces to match the application. Lenses in which both spherical aberration and coma are minimised are called bestform lenses.

Coma, or comatic aberration, derives its name from the comet-like appearance of the aberrated image. Coma occurs when an object off the optical axis of the lens is imaged, where rays pass through the lens at an angle to the axis θ. Rays that pass through the centre of a lens of focal length f are focused at a point with distance f tan θ from the axis. Rays passing through the outer margins of the lens are focused at different points, either further from the axis (positive coma) or closer to the axis (negative coma). In general, a bundle of parallel rays passing through the lens at a fixed distance from the centre of the lens are focused to a ring-shaped image in the focal plane, known as a <hl> comatic circle <hl>. The sum of all these circles results in a V-shaped or comet-like flare. As with spherical aberration, coma can be minimised (and in some cases eliminated) by choosing the curvature of the two lens surfaces to match the application. Lenses in which both spherical aberration and coma are minimised are called bestform lenses.

In general, a bundle of parallel rays passing through the lens at a fixed distance from the centre of the lens are focused to a ring-shaped image in the focal plane, known as a <hl> comatic circle <hl> .


Question: Comatic abberation results in what kind of appearance in it's aberrated images?

Answer: comet-like

<hl> Coma, or comatic aberration, derives its name from the comet-like appearance of the aberrated image. <hl> Coma occurs when an object off the optical axis of the lens is imaged, where rays pass through the lens at an angle to the axis θ. Rays that pass through the centre of a lens of focal length f are focused at a point with distance f tan θ from the axis. Rays passing through the outer margins of the lens are focused at different points, either further from the axis (positive coma) or closer to the axis (negative coma). In general, a bundle of parallel rays passing through the lens at a fixed distance from the centre of the lens are focused to a ring-shaped image in the focal plane, known as a comatic circle. The sum of all these circles results in a V-shaped or comet-like flare. As with spherical aberration, coma can be minimised (and in some cases eliminated) by choosing the curvature of the two lens surfaces to match the application. Lenses in which both spherical aberration and coma are minimised are called bestform lenses.

Coma, or comatic aberration, derives its name from the <hl> comet-like <hl> appearance of the aberrated image. Coma occurs when an object off the optical axis of the lens is imaged, where rays pass through the lens at an angle to the axis θ. Rays that pass through the centre of a lens of focal length f are focused at a point with distance f tan θ from the axis. Rays passing through the outer margins of the lens are focused at different points, either further from the axis (positive coma) or closer to the axis (negative coma). In general, a bundle of parallel rays passing through the lens at a fixed distance from the centre of the lens are focused to a ring-shaped image in the focal plane, known as a comatic circle. The sum of all these circles results in a V-shaped or comet-like flare. As with spherical aberration, coma can be minimised (and in some cases eliminated) by choosing the curvature of the two lens surfaces to match the application. Lenses in which both spherical aberration and coma are minimised are called bestform lenses.


Question: What are lenses classified as when effects such as spherical aberration and coma are minimized?

Answer: bestform

Coma, or comatic aberration, derives its name from the comet-like appearance of the aberrated image. Coma occurs when an object off the optical axis of the lens is imaged, where rays pass through the lens at an angle to the axis θ. Rays that pass through the centre of a lens of focal length f are focused at a point with distance f tan θ from the axis. Rays passing through the outer margins of the lens are focused at different points, either further from the axis (positive coma) or closer to the axis (negative coma). In general, a bundle of parallel rays passing through the lens at a fixed distance from the centre of the lens are focused to a ring-shaped image in the focal plane, known as a comatic circle. The sum of all these circles results in a V-shaped or comet-like flare. As with spherical aberration, coma can be minimised (and in some cases eliminated) by choosing the curvature of the two lens surfaces to match the application. <hl> Lenses in which both spherical aberration and coma are minimised are called bestform lenses. <hl>

Coma, or comatic aberration, derives its name from the comet-like appearance of the aberrated image. Coma occurs when an object off the optical axis of the lens is imaged, where rays pass through the lens at an angle to the axis θ. Rays that pass through the centre of a lens of focal length f are focused at a point with distance f tan θ from the axis. Rays passing through the outer margins of the lens are focused at different points, either further from the axis (positive coma) or closer to the axis (negative coma). In general, a bundle of parallel rays passing through the lens at a fixed distance from the centre of the lens are focused to a ring-shaped image in the focal plane, known as a comatic circle. The sum of all these circles results in a V-shaped or comet-like flare. As with spherical aberration, coma can be minimised (and in some cases eliminated) by choosing the curvature of the two lens surfaces to match the application. Lenses in which both spherical aberration and coma are minimised are called <hl> bestform <hl> lenses.


Question: What are lenses classified by?

Lenses are classified by the curvature of the two optical surfaces. A lens is biconvex (or double convex, or just convex) if both surfaces are convex. If both surfaces have the same radius of curvature, the lens is equiconvex. A lens with two concave surfaces is biconcave (or just concave). If one of the surfaces is flat, the lens is plano-convex or plano-concave depending on the curvature of the other surface. A lens with one convex and one concave side is convex-concave or meniscus. It is this type of lens that is most commonly used in corrective lenses.

Answer: the curvature of the two optical surfaces

<hl> Lenses are classified by the curvature of the two optical surfaces . <hl> A lens is biconvex (or double convex, or just convex) if both surfaces are convex. If both surfaces have the same radius of curvature, the lens is equiconvex. A lens with two concave surfaces is biconcave (or just concave). If one of the surfaces is flat, the lens is plano-convex or plano-concave depending on the curvature of the other surface. A lens with one convex and one concave side is convex-concave or meniscus. It is this type of lens that is most commonly used in corrective lenses.

Lenses are classified by <hl> the curvature of the two optical surfaces <hl>. A lens is biconvex (or double convex, or just convex) if both surfaces are convex. If both surfaces have the same radius of curvature, the lens is equiconvex. A lens with two concave surfaces is biconcave (or just concave). If one of the surfaces is flat, the lens is plano-convex or plano-concave depending on the curvature of the other surface. A lens with one convex and one concave side is convex-concave or meniscus. It is this type of lens that is most commonly used in corrective lenses.

Lenses are classified by <hl> the curvature of the two optical surfaces <hl> .


Question: What is a biconvex lens?

Answer: both surfaces are convex

if both surfaces are convex .

Lenses are classified by the curvature of the two optical surfaces. A lens is biconvex (or double convex, or just convex) <hl> if both surfaces are convex . <hl> If both surfaces have the same radius of curvature, the lens is equiconvex. A lens with two concave surfaces is biconcave (or just concave). If one of the surfaces is flat, the lens is plano-convex or plano-concave depending on the curvature of the other surface. A lens with one convex and one concave side is convex-concave or meniscus. It is this type of lens that is most commonly used in corrective lenses.

Lenses are classified by the curvature of the two optical surfaces. A lens is biconvex (or double convex, or just convex) if <hl> both surfaces are convex <hl>. If both surfaces have the same radius of curvature, the lens is equiconvex. A lens with two concave surfaces is biconcave (or just concave). If one of the surfaces is flat, the lens is plano-convex or plano-concave depending on the curvature of the other surface. A lens with one convex and one concave side is convex-concave or meniscus. It is this type of lens that is most commonly used in corrective lenses.


Question: What does equiconvex mean?

Answer: both surfaces have the same radius of curvature

Lenses are classified by the curvature of the two optical surfaces. A lens is biconvex (or double convex, or just convex) if both surfaces are convex. <hl> If both surfaces have the same radius of curvature , the lens is equiconvex. <hl> A lens with two concave surfaces is biconcave (or just concave). If one of the surfaces is flat, the lens is plano-convex or plano-concave depending on the curvature of the other surface. A lens with one convex and one concave side is convex-concave or meniscus. It is this type of lens that is most commonly used in corrective lenses.

Lenses are classified by the curvature of the two optical surfaces. A lens is biconvex (or double convex, or just convex) if both surfaces are convex. If <hl> both surfaces have the same radius of curvature <hl>, the lens is equiconvex. A lens with two concave surfaces is biconcave (or just concave). If one of the surfaces is flat, the lens is plano-convex or plano-concave depending on the curvature of the other surface. A lens with one convex and one concave side is convex-concave or meniscus. It is this type of lens that is most commonly used in corrective lenses.

If <hl> both surfaces have the same radius of curvature <hl> , the lens is equiconvex.


Question: When is a biconcave lens?

Answer: lens with two concave surfaces

Lenses are classified by the curvature of the two optical surfaces. A lens is biconvex (or double convex, or just convex) if both surfaces are convex. If both surfaces have the same radius of curvature, the lens is equiconvex. <hl> A lens with two concave surfaces is biconcave (or just concave). <hl> If one of the surfaces is flat, the lens is plano-convex or plano-concave depending on the curvature of the other surface. A lens with one convex and one concave side is convex-concave or meniscus. It is this type of lens that is most commonly used in corrective lenses.

Lenses are classified by the curvature of the two optical surfaces. A lens is biconvex (or double convex, or just convex) if both surfaces are convex. If both surfaces have the same radius of curvature, the lens is equiconvex. A <hl> lens with two concave surfaces <hl> is biconcave (or just concave). If one of the surfaces is flat, the lens is plano-convex or plano-concave depending on the curvature of the other surface. A lens with one convex and one concave side is convex-concave or meniscus. It is this type of lens that is most commonly used in corrective lenses.


Question: What is plano-convex?

Answer: one of the surfaces is flat

Lenses are classified by the curvature of the two optical surfaces. A lens is biconvex (or double convex, or just convex) if both surfaces are convex. If both surfaces have the same radius of curvature, the lens is equiconvex. A lens with two concave surfaces is biconcave (or just concave). <hl> If one of the surfaces is flat , the lens is plano-convex or plano-concave depending on the curvature of the other surface. <hl> A lens with one convex and one concave side is convex-concave or meniscus. It is this type of lens that is most commonly used in corrective lenses.

Lenses are classified by the curvature of the two optical surfaces. A lens is biconvex (or double convex, or just convex) if both surfaces are convex. If both surfaces have the same radius of curvature, the lens is equiconvex. A lens with two concave surfaces is biconcave (or just concave). If <hl> one of the surfaces is flat <hl>, the lens is plano-convex or plano-concave depending on the curvature of the other surface. A lens with one convex and one concave side is convex-concave or meniscus. It is this type of lens that is most commonly used in corrective lenses.

If <hl> one of the surfaces is flat <hl> , the lens is plano-convex or plano-concave depending on the curvature of the other surface.


Question: What does a negative meniscus lens have?

Convex-concave (meniscus) lenses can be either positive or negative, depending on the relative curvatures of the two surfaces. A negative meniscus lens has a steeper concave surface and is thinner at the centre than at the periphery. Conversely, a positive meniscus lens has a steeper convex surface and is thicker at the centre than at the periphery. An ideal thin lens with two surfaces of equal curvature would have zero optical power, meaning that it would neither converge nor diverge light. All real lenses have nonzero thickness, however, which makes a real lens with identical curved surfaces slightly positive. To obtain exactly zero optical power, a meniscus lens must have slightly unequal curvatures to account for the effect of the lens' thickness.

Answer: steeper concave surface and is thinner at the centre than at the periphery

Convex-concave (meniscus) lenses can be either positive or negative, depending on the relative curvatures of the two surfaces. <hl> A negative meniscus lens has a steeper concave surface and is thinner at the centre than at the periphery . <hl> Conversely, a positive meniscus lens has a steeper convex surface and is thicker at the centre than at the periphery. An ideal thin lens with two surfaces of equal curvature would have zero optical power, meaning that it would neither converge nor diverge light. All real lenses have nonzero thickness, however, which makes a real lens with identical curved surfaces slightly positive. To obtain exactly zero optical power, a meniscus lens must have slightly unequal curvatures to account for the effect of the lens' thickness.

Convex-concave (meniscus) lenses can be either positive or negative, depending on the relative curvatures of the two surfaces. A negative meniscus lens has a <hl> steeper concave surface and is thinner at the centre than at the periphery <hl>. Conversely, a positive meniscus lens has a steeper convex surface and is thicker at the centre than at the periphery. An ideal thin lens with two surfaces of equal curvature would have zero optical power, meaning that it would neither converge nor diverge light. All real lenses have nonzero thickness, however, which makes a real lens with identical curved surfaces slightly positive. To obtain exactly zero optical power, a meniscus lens must have slightly unequal curvatures to account for the effect of the lens' thickness.

A negative meniscus lens has a <hl> steeper concave surface and is thinner at the centre than at the periphery <hl> .


Question: What determines if convex-concave lenses are positive or negative?

Answer: the relative curvatures of the two surfaces

<hl> Convex-concave (meniscus) lenses can be either positive or negative, depending on the relative curvatures of the two surfaces . <hl> A negative meniscus lens has a steeper concave surface and is thinner at the centre than at the periphery. Conversely, a positive meniscus lens has a steeper convex surface and is thicker at the centre than at the periphery. An ideal thin lens with two surfaces of equal curvature would have zero optical power, meaning that it would neither converge nor diverge light. All real lenses have nonzero thickness, however, which makes a real lens with identical curved surfaces slightly positive. To obtain exactly zero optical power, a meniscus lens must have slightly unequal curvatures to account for the effect of the lens' thickness.

Convex-concave (meniscus) lenses can be either positive or negative, depending on <hl> the relative curvatures of the two surfaces <hl>. A negative meniscus lens has a steeper concave surface and is thinner at the centre than at the periphery. Conversely, a positive meniscus lens has a steeper convex surface and is thicker at the centre than at the periphery. An ideal thin lens with two surfaces of equal curvature would have zero optical power, meaning that it would neither converge nor diverge light. All real lenses have nonzero thickness, however, which makes a real lens with identical curved surfaces slightly positive. To obtain exactly zero optical power, a meniscus lens must have slightly unequal curvatures to account for the effect of the lens' thickness.

Convex-concave (meniscus) lenses can be either positive or negative, depending on <hl> the relative curvatures of the two surfaces <hl> .


Question: What does a positive meniscus lens have?

Answer: a steeper convex surface and is thicker at the centre than at the periphery

Convex-concave (meniscus) lenses can be either positive or negative, depending on the relative curvatures of the two surfaces. A negative meniscus lens has a steeper concave surface and is thinner at the centre than at the periphery. <hl> Conversely, a positive meniscus lens has a steeper convex surface and is thicker at the centre than at the periphery . <hl> An ideal thin lens with two surfaces of equal curvature would have zero optical power, meaning that it would neither converge nor diverge light. All real lenses have nonzero thickness, however, which makes a real lens with identical curved surfaces slightly positive. To obtain exactly zero optical power, a meniscus lens must have slightly unequal curvatures to account for the effect of the lens' thickness.

Convex-concave (meniscus) lenses can be either positive or negative, depending on the relative curvatures of the two surfaces. A negative meniscus lens has a steeper concave surface and is thinner at the centre than at the periphery. Conversely, a positive meniscus lens has <hl> a steeper convex surface and is thicker at the centre than at the periphery <hl>. An ideal thin lens with two surfaces of equal curvature would have zero optical power, meaning that it would neither converge nor diverge light. All real lenses have nonzero thickness, however, which makes a real lens with identical curved surfaces slightly positive. To obtain exactly zero optical power, a meniscus lens must have slightly unequal curvatures to account for the effect of the lens' thickness.

Conversely, a positive meniscus lens has <hl> a steeper convex surface and is thicker at the centre than at the periphery <hl> .


Question: What do all real lenses have?

Answer: nonzero thickness

Convex-concave (meniscus) lenses can be either positive or negative, depending on the relative curvatures of the two surfaces. A negative meniscus lens has a steeper concave surface and is thinner at the centre than at the periphery. Conversely, a positive meniscus lens has a steeper convex surface and is thicker at the centre than at the periphery. An ideal thin lens with two surfaces of equal curvature would have zero optical power, meaning that it would neither converge nor diverge light. <hl> All real lenses have nonzero thickness , however, which makes a real lens with identical curved surfaces slightly positive. <hl> To obtain exactly zero optical power, a meniscus lens must have slightly unequal curvatures to account for the effect of the lens' thickness.

Convex-concave (meniscus) lenses can be either positive or negative, depending on the relative curvatures of the two surfaces. A negative meniscus lens has a steeper concave surface and is thinner at the centre than at the periphery. Conversely, a positive meniscus lens has a steeper convex surface and is thicker at the centre than at the periphery. An ideal thin lens with two surfaces of equal curvature would have zero optical power, meaning that it would neither converge nor diverge light. All real lenses have <hl> nonzero thickness <hl>, however, which makes a real lens with identical curved surfaces slightly positive. To obtain exactly zero optical power, a meniscus lens must have slightly unequal curvatures to account for the effect of the lens' thickness.

All real lenses have <hl> nonzero thickness <hl> , however, which makes a real lens with identical curved surfaces slightly positive.


Question: How do you obtain exactly zero optical power?

Answer: a meniscus lens must have slightly unequal curvatures

Convex-concave (meniscus) lenses can be either positive or negative, depending on the relative curvatures of the two surfaces. A negative meniscus lens has a steeper concave surface and is thinner at the centre than at the periphery. Conversely, a positive meniscus lens has a steeper convex surface and is thicker at the centre than at the periphery. An ideal thin lens with two surfaces of equal curvature would have zero optical power, meaning that it would neither converge nor diverge light. All real lenses have nonzero thickness, however, which makes a real lens with identical curved surfaces slightly positive. <hl> To obtain exactly zero optical power, a meniscus lens must have slightly unequal curvatures to account for the effect of the lens' thickness. <hl>

Convex-concave (meniscus) lenses can be either positive or negative, depending on the relative curvatures of the two surfaces. A negative meniscus lens has a steeper concave surface and is thinner at the centre than at the periphery. Conversely, a positive meniscus lens has a steeper convex surface and is thicker at the centre than at the periphery. An ideal thin lens with two surfaces of equal curvature would have zero optical power, meaning that it would neither converge nor diverge light. All real lenses have nonzero thickness, however, which makes a real lens with identical curved surfaces slightly positive. To obtain exactly zero optical power, <hl> a meniscus lens must have slightly unequal curvatures <hl> to account for the effect of the lens' thickness.


Question: What does a positive or converging lens in air do?

As mentioned above, a positive or converging lens in air focuses a collimated beam travelling along the lens axis to a spot (known as the focal point) at a distance f from the lens. Conversely, a point source of light placed at the focal point is converted into a collimated beam by the lens. These two cases are examples of image formation in lenses. In the former case, an object at an infinite distance (as represented by a collimated beam of waves) is focused to an image at the focal point of the lens. In the latter, an object at the focal length distance from the lens is imaged at infinity. The plane perpendicular to the lens axis situated at a distance f from the lens is called the focal plane.

Answer: focuses a collimated beam

<hl> As mentioned above, a positive or converging lens in air focuses a collimated beam travelling along the lens axis to a spot (known as the focal point) at a distance f from the lens. <hl> Conversely, a point source of light placed at the focal point is converted into a collimated beam by the lens. These two cases are examples of image formation in lenses. In the former case, an object at an infinite distance (as represented by a collimated beam of waves) is focused to an image at the focal point of the lens. In the latter, an object at the focal length distance from the lens is imaged at infinity. The plane perpendicular to the lens axis situated at a distance f from the lens is called the focal plane.

As mentioned above, a positive or converging lens in air <hl> focuses a collimated beam <hl> travelling along the lens axis to a spot (known as the focal point) at a distance f from the lens. Conversely, a point source of light placed at the focal point is converted into a collimated beam by the lens. These two cases are examples of image formation in lenses. In the former case, an object at an infinite distance (as represented by a collimated beam of waves) is focused to an image at the focal point of the lens. In the latter, an object at the focal length distance from the lens is imaged at infinity. The plane perpendicular to the lens axis situated at a distance f from the lens is called the focal plane.


Question: What is the focal plane?

Answer: The plane perpendicular to the lens axis situated at a distance f from the lens is called the focal plane.

As mentioned above, a positive or converging lens in air focuses a collimated beam travelling along the lens axis to a spot (known as the focal point) at a distance f from the lens. Conversely, a point source of light placed at the focal point is converted into a collimated beam by the lens. These two cases are examples of image formation in lenses. In the former case, an object at an infinite distance (as represented by a collimated beam of waves) is focused to an image at the focal point of the lens. In the latter, an object at the focal length distance from the lens is imaged at infinity. <hl> The plane perpendicular to the lens axis situated at a distance f from the lens is called the focal plane. <hl>


Question: What is a point source of light placed at the focal point converted into?

Answer: collimated beam by the lens

As mentioned above, a positive or converging lens in air focuses a collimated beam travelling along the lens axis to a spot (known as the focal point) at a distance f from the lens. <hl> Conversely, a point source of light placed at the focal point is converted into a collimated beam by the lens . <hl> These two cases are examples of image formation in lenses. In the former case, an object at an infinite distance (as represented by a collimated beam of waves) is focused to an image at the focal point of the lens. In the latter, an object at the focal length distance from the lens is imaged at infinity. The plane perpendicular to the lens axis situated at a distance f from the lens is called the focal plane.

As mentioned above, a positive or converging lens in air focuses a collimated beam travelling along the lens axis to a spot (known as the focal point) at a distance f from the lens. Conversely, a point source of light placed at the focal point is converted into a <hl> collimated beam by the lens <hl>. These two cases are examples of image formation in lenses. In the former case, an object at an infinite distance (as represented by a collimated beam of waves) is focused to an image at the focal point of the lens. In the latter, an object at the focal length distance from the lens is imaged at infinity. The plane perpendicular to the lens axis situated at a distance f from the lens is called the focal plane.

Conversely, a point source of light placed at the focal point is converted into a <hl> collimated beam by the lens <hl> .


Question: How is an object at the focal length distance from the lens imaged?

Answer: at infinity

As mentioned above, a positive or converging lens in air focuses a collimated beam travelling along the lens axis to a spot (known as the focal point) at a distance f from the lens. Conversely, a point source of light placed at the focal point is converted into a collimated beam by the lens. These two cases are examples of image formation in lenses. In the former case, an object at an infinite distance (as represented by a collimated beam of waves) is focused to an image at the focal point of the lens. <hl> In the latter, an object at the focal length distance from the lens is imaged at infinity . <hl> The plane perpendicular to the lens axis situated at a distance f from the lens is called the focal plane.

As mentioned above, a positive or converging lens in air focuses a collimated beam travelling along the lens axis to a spot (known as the focal point) at a distance f from the lens. Conversely, a point source of light placed at the focal point is converted into a collimated beam by the lens. These two cases are examples of image formation in lenses. In the former case, an object at an infinite distance (as represented by a collimated beam of waves) is focused to an image at the focal point of the lens. In the latter, an object at the focal length distance from the lens is imaged <hl> at infinity <hl>. The plane perpendicular to the lens axis situated at a distance f from the lens is called the focal plane.

In the latter, an object at the focal length distance from the lens is imaged <hl> at infinity <hl> .


Question: What do the signs of the lens' radii of curvature indicate?

The signs of the lens' radii of curvature indicate whether the corresponding surfaces are convex or concave. The sign convention used to represent this varies, but in this article a positive R indicates a surface's center of curvature is further along in the direction of the ray travel (right, in the accompanying diagrams), while negative R means that rays reaching the surface have already passed the center of curvature. Consequently, for external lens surfaces as diagrammed above, R1 > 0 and  R2 < 0 indicate convex surfaces (used to converge light in a positive lens), while R1 < 0 and  R2 > 0 indicate concave surfaces. The reciprocal of the radius of curvature is called the curvature. A flat surface has zero curvature, and its radius of curvature  is infinity.

Answer: whether the corresponding surfaces are convex or concave

<hl> The signs of the lens' radii of curvature indicate whether the corresponding surfaces are convex or concave . <hl> The sign convention used to represent this varies, but in this article a positive R indicates a surface's center of curvature is further along in the direction of the ray travel (right, in the accompanying diagrams), while negative R means that rays reaching the surface have already passed the center of curvature. Consequently, for external lens surfaces as diagrammed above, R1 > 0 and R2 < 0 indicate convex surfaces (used to converge light in a positive lens), while R1 < 0 and R2 > 0 indicate concave surfaces. The reciprocal of the radius of curvature is called the curvature. A flat surface has zero curvature, and its radius of curvature is infinity.

The signs of the lens' radii of curvature indicate <hl> whether the corresponding surfaces are convex or concave <hl>. The sign convention used to represent this varies, but in this article a positive R indicates a surface's center of curvature is further along in the direction of the ray travel (right, in the accompanying diagrams), while negative R means that rays reaching the surface have already passed the center of curvature. Consequently, for external lens surfaces as diagrammed above, R1 > 0 and R2 < 0 indicate convex surfaces (used to converge light in a positive lens), while R1 < 0 and R2 > 0 indicate concave surfaces. The reciprocal of the radius of curvature is called the curvature. A flat surface has zero curvature, and its radius of curvature is infinity.

The signs of the lens' radii of curvature indicate <hl> whether the corresponding surfaces are convex or concave <hl> .


Question: What does negative R mean?

Answer: rays reaching the surface have already passed the center of curvature

The signs of the lens' radii of curvature indicate whether the corresponding surfaces are convex or concave. <hl> The sign convention used to represent this varies, but in this article a positive R indicates a surface's center of curvature is further along in the direction of the ray travel (right, in the accompanying diagrams), while negative R means that rays reaching the surface have already passed the center of curvature . <hl> Consequently, for external lens surfaces as diagrammed above, R1 > 0 and R2 < 0 indicate convex surfaces (used to converge light in a positive lens), while R1 < 0 and R2 > 0 indicate concave surfaces. The reciprocal of the radius of curvature is called the curvature. A flat surface has zero curvature, and its radius of curvature is infinity.

The signs of the lens' radii of curvature indicate whether the corresponding surfaces are convex or concave. The sign convention used to represent this varies, but in this article a positive R indicates a surface's center of curvature is further along in the direction of the ray travel (right, in the accompanying diagrams), while negative R means that <hl> rays reaching the surface have already passed the center of curvature <hl>. Consequently, for external lens surfaces as diagrammed above, R1 > 0 and R2 < 0 indicate convex surfaces (used to converge light in a positive lens), while R1 < 0 and R2 > 0 indicate concave surfaces. The reciprocal of the radius of curvature is called the curvature. A flat surface has zero curvature, and its radius of curvature is infinity.

The sign convention used to represent this varies, but in this article a positive R indicates a surface's center of curvature is further along in the direction of the ray travel (right, in the accompanying diagrams), while negative R means that <hl> rays reaching the surface have already passed the center of curvature <hl> .


Question: What does a positive R indicate?

Answer: a surface's center of curvature is further along in the direction of the ray travel

The signs of the lens' radii of curvature indicate whether the corresponding surfaces are convex or concave. <hl> The sign convention used to represent this varies, but in this article a positive R indicates a surface's center of curvature is further along in the direction of the ray travel (right, in the accompanying diagrams), while negative R means that rays reaching the surface have already passed the center of curvature. <hl> Consequently, for external lens surfaces as diagrammed above, R1 > 0 and R2 < 0 indicate convex surfaces (used to converge light in a positive lens), while R1 < 0 and R2 > 0 indicate concave surfaces. The reciprocal of the radius of curvature is called the curvature. A flat surface has zero curvature, and its radius of curvature is infinity.

The signs of the lens' radii of curvature indicate whether the corresponding surfaces are convex or concave. The sign convention used to represent this varies, but in this article a positive R indicates <hl> a surface's center of curvature is further along in the direction of the ray travel <hl> (right, in the accompanying diagrams), while negative R means that rays reaching the surface have already passed the center of curvature. Consequently, for external lens surfaces as diagrammed above, R1 > 0 and R2 < 0 indicate convex surfaces (used to converge light in a positive lens), while R1 < 0 and R2 > 0 indicate concave surfaces. The reciprocal of the radius of curvature is called the curvature. A flat surface has zero curvature, and its radius of curvature is infinity.


Question: What does R1 > 0 and R2 < 0 indicate?

Answer: convex surfaces

The signs of the lens' radii of curvature indicate whether the corresponding surfaces are convex or concave. The sign convention used to represent this varies, but in this article a positive R indicates a surface's center of curvature is further along in the direction of the ray travel (right, in the accompanying diagrams), while negative R means that rays reaching the surface have already passed the center of curvature. <hl> Consequently, for external lens surfaces as diagrammed above, R1 > 0 and R2 < 0 indicate convex surfaces (used to converge light in a positive lens), while R1 < 0 and R2 > 0 indicate concave surfaces. <hl> The reciprocal of the radius of curvature is called the curvature. A flat surface has zero curvature, and its radius of curvature is infinity.

The signs of the lens' radii of curvature indicate whether the corresponding surfaces are convex or concave. The sign convention used to represent this varies, but in this article a positive R indicates a surface's center of curvature is further along in the direction of the ray travel (right, in the accompanying diagrams), while negative R means that rays reaching the surface have already passed the center of curvature. Consequently, for external lens surfaces as diagrammed above, R1 > 0 and R2 < 0 indicate <hl> convex surfaces <hl> (used to converge light in a positive lens), while R1 < 0 and R2 > 0 indicate concave surfaces. The reciprocal of the radius of curvature is called the curvature. A flat surface has zero curvature, and its radius of curvature is infinity.


Question: What does R1 < 0 and R2 > 0 indicate?

Answer: concave surfaces

The signs of the lens' radii of curvature indicate whether the corresponding surfaces are convex or concave. The sign convention used to represent this varies, but in this article a positive R indicates a surface's center of curvature is further along in the direction of the ray travel (right, in the accompanying diagrams), while negative R means that rays reaching the surface have already passed the center of curvature. <hl> Consequently, for external lens surfaces as diagrammed above, R1 > 0 and R2 < 0 indicate convex surfaces (used to converge light in a positive lens), while R1 < 0 and R2 > 0 indicate concave surfaces . <hl> The reciprocal of the radius of curvature is called the curvature. A flat surface has zero curvature, and its radius of curvature is infinity.

The signs of the lens' radii of curvature indicate whether the corresponding surfaces are convex or concave. The sign convention used to represent this varies, but in this article a positive R indicates a surface's center of curvature is further along in the direction of the ray travel (right, in the accompanying diagrams), while negative R means that rays reaching the surface have already passed the center of curvature. Consequently, for external lens surfaces as diagrammed above, R1 > 0 and R2 < 0 indicate convex surfaces (used to converge light in a positive lens), while R1 < 0 and R2 > 0 indicate <hl> concave surfaces <hl>. The reciprocal of the radius of curvature is called the curvature. A flat surface has zero curvature, and its radius of curvature is infinity.

Consequently, for external lens surfaces as diagrammed above, R1 > 0 and R2 < 0 indicate convex surfaces (used to converge light in a positive lens), while R1 < 0 and R2 > 0 indicate <hl> concave surfaces <hl> .


Question: If S2 is negative, what does this indicate?

In some cases S2 is negative, indicating that the image is formed on the opposite side of the lens from where those rays are being considered. Since the diverging light rays emanating from the lens never come into focus, and those rays are not physically present at the point where they appear to form an image, this is called a virtual image. Unlike real images, a virtual image cannot be projected on a screen, but appears to an observer looking through the lens as if it were a real object at the location of that virtual image. Likewise, it appears to a subsequent lens as if it were an object at that location, so that second lens could again focus that light into a real image, S1 then being measured from the virtual image location behind the first lens to the second lens. This is exactly what the eye does when looking through a magnifying glass. The magnifying glass creates a (magnified) virtual image behind the magnifying glass, but those rays are then re-imaged by the lens of the eye to create a real image on the retina.

Answer: image is formed on the opposite side of the lens from where those rays are being considered

<hl> In some cases S2 is negative, indicating that the image is formed on the opposite side of the lens from where those rays are being considered . <hl> Since the diverging light rays emanating from the lens never come into focus, and those rays are not physically present at the point where they appear to form an image, this is called a virtual image. Unlike real images, a virtual image cannot be projected on a screen, but appears to an observer looking through the lens as if it were a real object at the location of that virtual image. Likewise, it appears to a subsequent lens as if it were an object at that location, so that second lens could again focus that light into a real image, S1 then being measured from the virtual image location behind the first lens to the second lens. This is exactly what the eye does when looking through a magnifying glass. The magnifying glass creates a (magnified) virtual image behind the magnifying glass, but those rays are then re-imaged by the lens of the eye to create a real image on the retina.

In some cases S2 is negative, indicating that the <hl> image is formed on the opposite side of the lens from where those rays are being considered <hl>. Since the diverging light rays emanating from the lens never come into focus, and those rays are not physically present at the point where they appear to form an image, this is called a virtual image. Unlike real images, a virtual image cannot be projected on a screen, but appears to an observer looking through the lens as if it were a real object at the location of that virtual image. Likewise, it appears to a subsequent lens as if it were an object at that location, so that second lens could again focus that light into a real image, S1 then being measured from the virtual image location behind the first lens to the second lens. This is exactly what the eye does when looking through a magnifying glass. The magnifying glass creates a (magnified) virtual image behind the magnifying glass, but those rays are then re-imaged by the lens of the eye to create a real image on the retina.

In some cases S2 is negative, indicating that the <hl> image is formed on the opposite side of the lens from where those rays are being considered <hl> .


Question: What can a virtual image not do?

Answer: be projected on a screen

In some cases S2 is negative, indicating that the image is formed on the opposite side of the lens from where those rays are being considered. Since the diverging light rays emanating from the lens never come into focus, and those rays are not physically present at the point where they appear to form an image, this is called a virtual image. <hl> Unlike real images, a virtual image cannot be projected on a screen , but appears to an observer looking through the lens as if it were a real object at the location of that virtual image. <hl> Likewise, it appears to a subsequent lens as if it were an object at that location, so that second lens could again focus that light into a real image, S1 then being measured from the virtual image location behind the first lens to the second lens. This is exactly what the eye does when looking through a magnifying glass. The magnifying glass creates a (magnified) virtual image behind the magnifying glass, but those rays are then re-imaged by the lens of the eye to create a real image on the retina.

In some cases S2 is negative, indicating that the image is formed on the opposite side of the lens from where those rays are being considered. Since the diverging light rays emanating from the lens never come into focus, and those rays are not physically present at the point where they appear to form an image, this is called a virtual image. Unlike real images, a virtual image cannot <hl> be projected on a screen <hl>, but appears to an observer looking through the lens as if it were a real object at the location of that virtual image. Likewise, it appears to a subsequent lens as if it were an object at that location, so that second lens could again focus that light into a real image, S1 then being measured from the virtual image location behind the first lens to the second lens. This is exactly what the eye does when looking through a magnifying glass. The magnifying glass creates a (magnified) virtual image behind the magnifying glass, but those rays are then re-imaged by the lens of the eye to create a real image on the retina.

Unlike real images, a virtual image cannot <hl> be projected on a screen <hl> , but appears to an observer looking through the lens as if it were a real object at the location of that virtual image.


Question: What does a virtual image attempting to be projected appear like to an observer looking through the lens?

Answer: a real object at the location of that virtual image

In some cases S2 is negative, indicating that the image is formed on the opposite side of the lens from where those rays are being considered. Since the diverging light rays emanating from the lens never come into focus, and those rays are not physically present at the point where they appear to form an image, this is called a virtual image. <hl> Unlike real images, a virtual image cannot be projected on a screen, but appears to an observer looking through the lens as if it were a real object at the location of that virtual image . <hl> Likewise, it appears to a subsequent lens as if it were an object at that location, so that second lens could again focus that light into a real image, S1 then being measured from the virtual image location behind the first lens to the second lens. This is exactly what the eye does when looking through a magnifying glass. The magnifying glass creates a (magnified) virtual image behind the magnifying glass, but those rays are then re-imaged by the lens of the eye to create a real image on the retina.

In some cases S2 is negative, indicating that the image is formed on the opposite side of the lens from where those rays are being considered. Since the diverging light rays emanating from the lens never come into focus, and those rays are not physically present at the point where they appear to form an image, this is called a virtual image. Unlike real images, a virtual image cannot be projected on a screen, but appears to an observer looking through the lens as if it were <hl> a real object at the location of that virtual image <hl>. Likewise, it appears to a subsequent lens as if it were an object at that location, so that second lens could again focus that light into a real image, S1 then being measured from the virtual image location behind the first lens to the second lens. This is exactly what the eye does when looking through a magnifying glass. The magnifying glass creates a (magnified) virtual image behind the magnifying glass, but those rays are then re-imaged by the lens of the eye to create a real image on the retina.

Unlike real images, a virtual image cannot be projected on a screen, but appears to an observer looking through the lens as if it were <hl> a real object at the location of that virtual image <hl> .


Question: What does a magnifying glass create?

Answer: virtual image behind the magnifying glass

In some cases S2 is negative, indicating that the image is formed on the opposite side of the lens from where those rays are being considered. Since the diverging light rays emanating from the lens never come into focus, and those rays are not physically present at the point where they appear to form an image, this is called a virtual image. Unlike real images, a virtual image cannot be projected on a screen, but appears to an observer looking through the lens as if it were a real object at the location of that virtual image. Likewise, it appears to a subsequent lens as if it were an object at that location, so that second lens could again focus that light into a real image, S1 then being measured from the virtual image location behind the first lens to the second lens. This is exactly what the eye does when looking through a magnifying glass. <hl> The magnifying glass creates a (magnified) virtual image behind the magnifying glass , but those rays are then re-imaged by the lens of the eye to create a real image on the retina. <hl>

In some cases S2 is negative, indicating that the image is formed on the opposite side of the lens from where those rays are being considered. Since the diverging light rays emanating from the lens never come into focus, and those rays are not physically present at the point where they appear to form an image, this is called a virtual image. Unlike real images, a virtual image cannot be projected on a screen, but appears to an observer looking through the lens as if it were a real object at the location of that virtual image. Likewise, it appears to a subsequent lens as if it were an object at that location, so that second lens could again focus that light into a real image, S1 then being measured from the virtual image location behind the first lens to the second lens. This is exactly what the eye does when looking through a magnifying glass. The magnifying glass creates a (magnified) <hl> virtual image behind the magnifying glass <hl>, but those rays are then re-imaged by the lens of the eye to create a real image on the retina.

The magnifying glass creates a (magnified) <hl> virtual image behind the magnifying glass <hl> , but those rays are then re-imaged by the lens of the eye to create a real image on the retina.


Question: What happened between 1917 and 1939?

During the British Raj, the Kingdom of Manipur was one of the princely states.[page needed] Between 1917 and 1939, the people of Manipur pressed for their rights against the British Rule. By the late 1930s, the princely state of Manipur negotiated with the British administration its preference to be part of India, rather than Burma.[page needed] These negotiations were cut short with the outbreak of World War II. On 21 September 1949, Maharaja Budhachandra signed a Treaty of Accession merging the kingdom into India. This merger is disputed by groups in Manipur as having been completed without consensus and under duress.

Answer: Between 1917 and 1939, the people of Manipur pressed for their rights against the British Rule.

<hl> During the British Raj, the Kingdom of Manipur was one of the princely states.[page needed] Between 1917 and 1939, the people of Manipur pressed for their rights against the British Rule. By the late 1930s, the princely state of Manipur negotiated with the British administration its preference to be part of India, rather than Burma.[page needed] These negotiations were cut short with the outbreak of World War II. <hl> On 21 September 1949, Maharaja Budhachandra signed a Treaty of Accession merging the kingdom into India. This merger is disputed by groups in Manipur as having been completed without consensus and under duress.

During the British Raj, the Kingdom of Manipur was one of the princely states.[page needed] <hl> Between 1917 and 1939, the people of Manipur pressed for their rights against the British Rule. <hl> By the late 1930s, the princely state of Manipur negotiated with the British administration its preference to be part of India, rather than Burma.[page needed] These negotiations were cut short with the outbreak of World War II. On 21 September 1949, Maharaja Budhachandra signed a Treaty of Accession merging the kingdom into India. This merger is disputed by groups in Manipur as having been completed without consensus and under duress.


Question: The state of Manipur wanted to be part of what?

Answer: the princely state of Manipur negotiated with the British administration its preference to be part of India, rather than Burma.

During the British Raj, the Kingdom of Manipur was one of the princely states.[page needed] Between 1917 and 1939, the people of Manipur pressed for their rights against the British Rule. <hl> By the late 1930s, the princely state of Manipur negotiated with the British administration its preference to be part of India, rather than Burma. [page needed] These negotiations were cut short with the outbreak of World War II. <hl> On 21 September 1949, Maharaja Budhachandra signed a Treaty of Accession merging the kingdom into India. This merger is disputed by groups in Manipur as having been completed without consensus and under duress.

During the British Raj, the Kingdom of Manipur was one of the princely states.[page needed] Between 1917 and 1939, the people of Manipur pressed for their rights against the British Rule. By the late 1930s, <hl> the princely state of Manipur negotiated with the British administration its preference to be part of India, rather than Burma. <hl>[page needed] These negotiations were cut short with the outbreak of World War II. On 21 September 1949, Maharaja Budhachandra signed a Treaty of Accession merging the kingdom into India. This merger is disputed by groups in Manipur as having been completed without consensus and under duress.

By the late 1930s, <hl> the princely state of Manipur negotiated with the British administration its preference to be part of India, rather than Burma. <hl> [page needed] These negotiations were cut short with the outbreak of World War II.


Question: Why were the negotiations cut short?

Answer: These negotiations were cut short with the outbreak of World War II.

During the British Raj, the Kingdom of Manipur was one of the princely states.[page needed] Between 1917 and 1939, the people of Manipur pressed for their rights against the British Rule. <hl> By the late 1930s, the princely state of Manipur negotiated with the British administration its preference to be part of India, rather than Burma.[page needed] These negotiations were cut short with the outbreak of World War II. On 21 September 1949, Maharaja Budhachandra signed a Treaty of Accession merging the kingdom into India. <hl> This merger is disputed by groups in Manipur as having been completed without consensus and under duress.

During the British Raj, the Kingdom of Manipur was one of the princely states.[page needed] Between 1917 and 1939, the people of Manipur pressed for their rights against the British Rule. By the late 1930s, the princely state of Manipur negotiated with the British administration its preference to be part of India, rather than Burma.[page needed] <hl> These negotiations were cut short with the outbreak of World War II. <hl> On 21 September 1949, Maharaja Budhachandra signed a Treaty of Accession merging the kingdom into India. This merger is disputed by groups in Manipur as having been completed without consensus and under duress.


Question: What treaty was signed?

Answer: On 21 September 1949, Maharaja Budhachandra signed a Treaty of Accession merging the kingdom into India.

During the British Raj, the Kingdom of Manipur was one of the princely states.[page needed] Between 1917 and 1939, the people of Manipur pressed for their rights against the British Rule. By the late 1930s, the princely state of Manipur negotiated with the British administration its preference to be part of India, rather than Burma.[page needed] These negotiations were cut short with the outbreak of World War II. <hl> On 21 September 1949, Maharaja Budhachandra signed a Treaty of Accession merging the kingdom into India. This merger is disputed by groups in Manipur as having been completed without consensus and under duress. <hl>

During the British Raj, the Kingdom of Manipur was one of the princely states.[page needed] Between 1917 and 1939, the people of Manipur pressed for their rights against the British Rule. By the late 1930s, the princely state of Manipur negotiated with the British administration its preference to be part of India, rather than Burma.[page needed] These negotiations were cut short with the outbreak of World War II. <hl> On 21 September 1949, Maharaja Budhachandra signed a Treaty of Accession merging the kingdom into India. <hl> This merger is disputed by groups in Manipur as having been completed without consensus and under duress.


Question: What were the different names for Manipur?

Neighbouring cultures each had differing names for Manipur and its people. The Shan or Pong called the area Cassay, the Burmese Kathe, and the Assamese Meklee. In the first treaty between the British East India Company and Meidingu Chingthangkhomba (Bhagyachandra) signed in 1762, the kingdom was recorded as Meckley. Bhagyachandra and his successors issued coins engraved with "Manipureshwar", or "lord of Manipur", and the British discarded the name Meckley. Later on, the work Dharani Samhita (1825–34) popularised the Sanskrit legends of the origin of Manipur's name.

Answer: The Shan or Pong called the area Cassay, the Burmese Kathe, and the Assamese Meklee.

Neighbouring cultures each had differing names for Manipur and its people. <hl> The Shan or Pong called the area Cassay, the Burmese Kathe, and the Assamese Meklee. In the first treaty between the British East India Company and Meidingu Chingthangkhomba (Bhagyachandra) signed in 1762, the kingdom was recorded as Meckley. <hl> Bhagyachandra and his successors issued coins engraved with "Manipureshwar", or "lord of Manipur", and the British discarded the name Meckley. Later on, the work Dharani Samhita (1825–34) popularised the Sanskrit legends of the origin of Manipur's name.

Neighbouring cultures each had differing names for Manipur and its people. <hl> The Shan or Pong called the area Cassay, the Burmese Kathe, and the Assamese Meklee. <hl> In the first treaty between the British East India Company and Meidingu Chingthangkhomba (Bhagyachandra) signed in 1762, the kingdom was recorded as Meckley. Bhagyachandra and his successors issued coins engraved with "Manipureshwar", or "lord of Manipur", and the British discarded the name Meckley. Later on, the work Dharani Samhita (1825–34) popularised the Sanskrit legends of the origin of Manipur's name.


Question: What did Bhagyachandra and his successors do?

Answer: Bhagyachandra and his successors issued coins engraved with "Manipureshwar", or "lord of Manipur", and the British discarded the name Meckley.

Neighbouring cultures each had differing names for Manipur and its people. The Shan or Pong called the area Cassay, the Burmese Kathe, and the Assamese Meklee. In the first treaty between the British East India Company and Meidingu Chingthangkhomba (Bhagyachandra) signed in 1762, the kingdom was recorded as Meckley. <hl> Bhagyachandra and his successors issued coins engraved with "Manipureshwar", or "lord of Manipur", and the British discarded the name Meckley. Later on, the work Dharani Samhita (1825–34) popularised the Sanskrit legends of the origin of Manipur's name. <hl>

Neighbouring cultures each had differing names for Manipur and its people. The Shan or Pong called the area Cassay, the Burmese Kathe, and the Assamese Meklee. In the first treaty between the British East India Company and Meidingu Chingthangkhomba (Bhagyachandra) signed in 1762, the kingdom was recorded as Meckley. <hl> Bhagyachandra and his successors issued coins engraved with "Manipureshwar", or "lord of Manipur", and the British discarded the name Meckley. <hl> Later on, the work Dharani Samhita (1825–34) popularised the Sanskrit legends of the origin of Manipur's name.


Question: What was the treaty between British East India and Meidingu?

Answer: In the first treaty between the British East India Company and Meidingu Chingthangkhomba (Bhagyachandra) signed in 1762, the kingdom was recorded as Meckley.

Neighbouring cultures each had differing names for Manipur and its people. The Shan or Pong called the area Cassay, the Burmese Kathe, and the Assamese Meklee. <hl> In the first treaty between the British East India Company and Meidingu Chingthangkhomba (Bhagyachandra) signed in 1762, the kingdom was recorded as Meckley. Bhagyachandra and his successors issued coins engraved with "Manipureshwar", or "lord of Manipur", and the British discarded the name Meckley. <hl> Later on, the work Dharani Samhita (1825–34) popularised the Sanskrit legends of the origin of Manipur's name.

Neighbouring cultures each had differing names for Manipur and its people. The Shan or Pong called the area Cassay, the Burmese Kathe, and the Assamese Meklee. <hl> In the first treaty between the British East India Company and Meidingu Chingthangkhomba (Bhagyachandra) signed in 1762, the kingdom was recorded as Meckley. <hl> Bhagyachandra and his successors issued coins engraved with "Manipureshwar", or "lord of Manipur", and the British discarded the name Meckley. Later on, the work Dharani Samhita (1825–34) popularised the Sanskrit legends of the origin of Manipur's name.


Question: What did Dharani Samhita do?

Answer: Later on, the work Dharani Samhita (1825–34) popularised the Sanskrit legends of the origin of Manipur's name.

Neighbouring cultures each had differing names for Manipur and its people. The Shan or Pong called the area Cassay, the Burmese Kathe, and the Assamese Meklee. In the first treaty between the British East India Company and Meidingu Chingthangkhomba (Bhagyachandra) signed in 1762, the kingdom was recorded as Meckley. Bhagyachandra and his successors issued coins engraved with "Manipureshwar", or "lord of Manipur", and the British discarded the name Meckley. <hl> Later on, the work Dharani Samhita (1825–34) popularised the Sanskrit legends of the origin of Manipur's name. <hl>


Question: When did the separatist movement begin?

A separatist movement has been active in Manipur since 1964, when United National Liberation Front was founded. Several groups have used violence toward achieving their goal of a sovereign Manipur. In addition, tribal peoples have demanded division of the present state into two or three Indian states along ethnic lines. This is considered one of India's "sensitive areas", due to its political troubles and isolated geography. Foreign travelers must gain permission from the government to enter the state.

Answer: A separatist movement has been active in Manipur since 1964, when United National Liberation Front was founded.

<hl> A separatist movement has been active in Manipur since 1964, when United National Liberation Front was founded. Several groups have used violence toward achieving their goal of a sovereign Manipur. <hl> In addition, tribal peoples have demanded division of the present state into two or three Indian states along ethnic lines. This is considered one of India's "sensitive areas", due to its political troubles and isolated geography. Foreign travelers must gain permission from the government to enter the state.

<hl> A separatist movement has been active in Manipur since 1964, when United National Liberation Front was founded. <hl> Several groups have used violence toward achieving their goal of a sovereign Manipur. In addition, tribal peoples have demanded division of the present state into two or three Indian states along ethnic lines. This is considered one of India's "sensitive areas", due to its political troubles and isolated geography. Foreign travelers must gain permission from the government to enter the state.


Question: What is being demanded?

Answer: tribal peoples have demanded division of the present state into two or three Indian states along ethnic lines.

A separatist movement has been active in Manipur since 1964, when United National Liberation Front was founded. Several groups have used violence toward achieving their goal of a sovereign Manipur. <hl> In addition, tribal peoples have demanded division of the present state into two or three Indian states along ethnic lines. This is considered one of India's "sensitive areas", due to its political troubles and isolated geography. <hl> Foreign travelers must gain permission from the government to enter the state.

A separatist movement has been active in Manipur since 1964, when United National Liberation Front was founded. Several groups have used violence toward achieving their goal of a sovereign Manipur. In addition, <hl> tribal peoples have demanded division of the present state into two or three Indian states along ethnic lines. <hl> This is considered one of India's "sensitive areas", due to its political troubles and isolated geography. Foreign travelers must gain permission from the government to enter the state.


Question: What kind of problems does India face?

Answer: This is considered one of India's "sensitive areas", due to its political troubles and isolated geography.

A separatist movement has been active in Manipur since 1964, when United National Liberation Front was founded. Several groups have used violence toward achieving their goal of a sovereign Manipur. In addition, tribal peoples have demanded division of the present state into two or three Indian states along ethnic lines. <hl> This is considered one of India's "sensitive areas", due to its political troubles and isolated geography. Foreign travelers must gain permission from the government to enter the state. <hl>

A separatist movement has been active in Manipur since 1964, when United National Liberation Front was founded. Several groups have used violence toward achieving their goal of a sovereign Manipur. In addition, tribal peoples have demanded division of the present state into two or three Indian states along ethnic lines. <hl> This is considered one of India's "sensitive areas", due to its political troubles and isolated geography. <hl> Foreign travelers must gain permission from the government to enter the state.


Question: What must travelers do?

Answer: Foreign travelers must gain permission from the government to enter the state.

A separatist movement has been active in Manipur since 1964, when United National Liberation Front was founded. Several groups have used violence toward achieving their goal of a sovereign Manipur. In addition, tribal peoples have demanded division of the present state into two or three Indian states along ethnic lines. This is considered one of India's "sensitive areas", due to its political troubles and isolated geography. <hl> Foreign travelers must gain permission from the government to enter the state. <hl>


Question: Who was the first armed group in Manipur?

Manipur has had a long record of insurgency and inter-ethnic violence. The first armed opposition group in Manipur, the United National Liberation Front (UNLF), was founded in 1964, which declared that it wanted to gain independence from India and form Manipur as a new country. Over time, many more groups formed in Manipur, each with different goals, and deriving support from diverse ethnic groups in Manipur. For example, in 1977 the People's Revolutionary Party of Kangleipak (PREPAK) was formed, the People's Liberation Army (PLA) was formed in 1978 which Human Rights Watch states as having received arms and training from China. In 1980, the Kangleipak Communist Party (KCP) was formed. These groups began a spree of bank robberies and attacks on police officers and government buildings. The state government appealed to the central government in New Delhi for support in combating this violence.

Answer: The first armed opposition group in Manipur, the United National Liberation Front (UNLF)

Manipur has had a long record of insurgency and inter-ethnic violence. <hl> The first armed opposition group in Manipur, the United National Liberation Front (UNLF) , was founded in 1964, which declared that it wanted to gain independence from India and form Manipur as a new country. <hl> Over time, many more groups formed in Manipur, each with different goals, and deriving support from diverse ethnic groups in Manipur. For example, in 1977 the People's Revolutionary Party of Kangleipak (PREPAK) was formed, the People's Liberation Army (PLA) was formed in 1978 which Human Rights Watch states as having received arms and training from China. In 1980, the Kangleipak Communist Party (KCP) was formed. These groups began a spree of bank robberies and attacks on police officers and government buildings. The state government appealed to the central government in New Delhi for support in combating this violence.

Manipur has had a long record of insurgency and inter-ethnic violence. <hl> The first armed opposition group in Manipur, the United National Liberation Front (UNLF) <hl>, was founded in 1964, which declared that it wanted to gain independence from India and form Manipur as a new country. Over time, many more groups formed in Manipur, each with different goals, and deriving support from diverse ethnic groups in Manipur. For example, in 1977 the People's Revolutionary Party of Kangleipak (PREPAK) was formed, the People's Liberation Army (PLA) was formed in 1978 which Human Rights Watch states as having received arms and training from China. In 1980, the Kangleipak Communist Party (KCP) was formed. These groups began a spree of bank robberies and attacks on police officers and government buildings. The state government appealed to the central government in New Delhi for support in combating this violence.

<hl> The first armed opposition group in Manipur, the United National Liberation Front (UNLF) <hl> , was founded in 1964, which declared that it wanted to gain independence from India and form Manipur as a new country.


Question: What group was formed in 1977?

Answer: in 1977 the People's Revolutionary Party of Kangleipak (PREPAK) was formed

Manipur has had a long record of insurgency and inter-ethnic violence. The first armed opposition group in Manipur, the United National Liberation Front (UNLF), was founded in 1964, which declared that it wanted to gain independence from India and form Manipur as a new country. Over time, many more groups formed in Manipur, each with different goals, and deriving support from diverse ethnic groups in Manipur. <hl> For example, in 1977 the People's Revolutionary Party of Kangleipak (PREPAK) was formed , the People's Liberation Army (PLA) was formed in 1978 which Human Rights Watch states as having received arms and training from China. <hl> In 1980, the Kangleipak Communist Party (KCP) was formed. These groups began a spree of bank robberies and attacks on police officers and government buildings. The state government appealed to the central government in New Delhi for support in combating this violence.

Manipur has had a long record of insurgency and inter-ethnic violence. The first armed opposition group in Manipur, the United National Liberation Front (UNLF), was founded in 1964, which declared that it wanted to gain independence from India and form Manipur as a new country. Over time, many more groups formed in Manipur, each with different goals, and deriving support from diverse ethnic groups in Manipur. For example, <hl> in 1977 the People's Revolutionary Party of Kangleipak (PREPAK) was formed <hl>, the People's Liberation Army (PLA) was formed in 1978 which Human Rights Watch states as having received arms and training from China. In 1980, the Kangleipak Communist Party (KCP) was formed. These groups began a spree of bank robberies and attacks on police officers and government buildings. The state government appealed to the central government in New Delhi for support in combating this violence.

For example, <hl> in 1977 the People's Revolutionary Party of Kangleipak (PREPAK) was formed <hl> , the People's Liberation Army (PLA) was formed in 1978 which Human Rights Watch states as having received arms and training from China.


Question: When was it founded and why?

Answer: was founded in 1964, which declared that it wanted to gain independence from India and form Manipur as a new country.

Manipur has had a long record of insurgency and inter-ethnic violence. <hl> The first armed opposition group in Manipur, the United National Liberation Front (UNLF), was founded in 1964, which declared that it wanted to gain independence from India and form Manipur as a new country. Over time, many more groups formed in Manipur, each with different goals, and deriving support from diverse ethnic groups in Manipur. <hl> For example, in 1977 the People's Revolutionary Party of Kangleipak (PREPAK) was formed, the People's Liberation Army (PLA) was formed in 1978 which Human Rights Watch states as having received arms and training from China. In 1980, the Kangleipak Communist Party (KCP) was formed. These groups began a spree of bank robberies and attacks on police officers and government buildings. The state government appealed to the central government in New Delhi for support in combating this violence.

Manipur has had a long record of insurgency and inter-ethnic violence. The first armed opposition group in Manipur, the United National Liberation Front (UNLF), <hl> was founded in 1964, which declared that it wanted to gain independence from India and form Manipur as a new country. <hl> Over time, many more groups formed in Manipur, each with different goals, and deriving support from diverse ethnic groups in Manipur. For example, in 1977 the People's Revolutionary Party of Kangleipak (PREPAK) was formed, the People's Liberation Army (PLA) was formed in 1978 which Human Rights Watch states as having received arms and training from China. In 1980, the Kangleipak Communist Party (KCP) was formed. These groups began a spree of bank robberies and attacks on police officers and government buildings. The state government appealed to the central government in New Delhi for support in combating this violence.


Question: When was PLA formed?

Answer: the People's Liberation Army (PLA) was formed in 1978 which Human Rights Watch states as having received arms and training from China.

Manipur has had a long record of insurgency and inter-ethnic violence. The first armed opposition group in Manipur, the United National Liberation Front (UNLF), was founded in 1964, which declared that it wanted to gain independence from India and form Manipur as a new country. Over time, many more groups formed in Manipur, each with different goals, and deriving support from diverse ethnic groups in Manipur. <hl> For example, in 1977 the People's Revolutionary Party of Kangleipak (PREPAK) was formed, the People's Liberation Army (PLA) was formed in 1978 which Human Rights Watch states as having received arms and training from China. In 1980, the Kangleipak Communist Party (KCP) was formed. <hl> These groups began a spree of bank robberies and attacks on police officers and government buildings. The state government appealed to the central government in New Delhi for support in combating this violence.

Manipur has had a long record of insurgency and inter-ethnic violence. The first armed opposition group in Manipur, the United National Liberation Front (UNLF), was founded in 1964, which declared that it wanted to gain independence from India and form Manipur as a new country. Over time, many more groups formed in Manipur, each with different goals, and deriving support from diverse ethnic groups in Manipur. For example, in 1977 the People's Revolutionary Party of Kangleipak (PREPAK) was formed, <hl> the People's Liberation Army (PLA) was formed in 1978 which Human Rights Watch states as having received arms and training from China. <hl> In 1980, the Kangleipak Communist Party (KCP) was formed. These groups began a spree of bank robberies and attacks on police officers and government buildings. The state government appealed to the central government in New Delhi for support in combating this violence.