Ray Diagrams - Concave Mirrors Reflection and the Ray Model of Light - Lesson 3 - Concave Mirrors Ray Diagrams - Concave Mirrors Spherical Aberration The theme of this unit has been that we see an object because light from the object travels to our eyes as we sight along a line at the object. Similarly, we see an image of an object because light from the object reflects off a mirror and travel to our eyes as we sight at the image location of the object. From these two basic premises, we have defined the image location as the location in space where light appears to diverge from. Ray diagrams have been a valuable tool for determining the path taken by light from the object to the mirror to our eyes. In this section of Lesson 3, we will investigate the method for drawing ray diagrams for objects placed at various locations in front of a concave mirror. To draw these diagrams, we will have to recall the two rules of reflection for concave mirrors: Any incident ray traveling parallel to the principal axis on the way to the mirror will pass through the focal point upon reflection. Any incident ray passing through the focal point on the way to the mirror will travel parallel to the principal axis upon reflection.

Earlier in this lesson, the following diagram was shown to illustrate the path of light from an object to mirror to an eye. In this diagram five incident rays are drawn along with their corresponding reflected rays. Each ray intersects at the image location and then diverges to the eye of an observer. Every observer would observe the same image location and every light ray would follow the law of reflection. Yet only two of these rays would be needed to determine the image location since it only requires two rays to find the intersection point. Of the five incident rays drawn, two of them correspond to the incident rays described by our two rules of reflection for concave mirrors. Because they are the easiest and most predictable pair of rays to draw, these will be the two rays used through the remainder of this lesson Step-by-Step Method for Drawing Ray Diagrams The method for drawing ray diagrams for concave mirror is described below. The method is applied to the task of drawing a ray diagram for an object located beyond the center of curvature (C) of a concave mirror. Yet the same method works for drawing a ray diagram for any object location. 1. Pick a point on the top of the object and draw two incident rays traveling towards the mirror.

Using a straight edge, accurately draw one ray so that it passes exactly through the focal point on the way to the mirror. Draw the second ray such that it travels exactly parallel to the principal axis. Place arrowheads upon the rays to indicate their direction of travel. 2. Once these incident rays strike the mirror, reflect them according to the two rules of reflection for concave mirrors. The ray that passes through the focal point on the way to the mirror will reflect and travel parallel to the principal axis. Use a straight edge to accurately draw its path. The ray that traveled parallel to the principal axis on the way to the mirror will reflect and travel through the focal point. Place arrowheads upon the rays to indicate their direction of travel. Extend the rays past their point of intersection. 3. Mark the image of the top of the object. The image point of the top of the object is the point where the two reflected rays intersect. If your were to draw a third pair of incident and reflected rays, then the third reflected ray would also pass through this point. This is merely the point where all light from the top of the object would intersect upon reflecting off the mirror.

Of course, the rest of the object has an image as well and it can be found by applying the same three steps to another chosen point. (See note below .) 4. Repeat the process for the bottom of the object. The goal of a ray diagram is to determine the location, size, orientation, and type of image that is formed by the concave mirror. Typically, this requires determining where the image of the upper and lower extreme of the object is located and then tracing the entire image. After completing the first three steps, only the image location of the top extreme of the object has been found. Thus, the process must be repeated for the point on the bottom of the object. If the bottom of the object lies upon the principal axis (as it does in this example), then the image of this point will also lie upon the principal axis and be the same distance from the mirror as the image of the top of the object. At this point the entire image can be filled in. Some students have difficulty understanding how the entire image of an object can be deduced once a single point on the image has been determined.

If the object is a vertically aligned object (such as the arrow object used in the example below), then the process is easy. The image is merely a vertical line. In theory, it would be necessary to pick each point on the object and draw a separate ray diagram to determine the location of the image of that point. That would require a lot of ray diagrams as illustrated below. Fortunately, a shortcut exists. If the object is a vertical line, then the image is also a vertical line. For our purposes, we will only deal with the simpler situations in which the object is a vertical line that has its bottom located upon the principal axis. For such simplified situations, the image is a vertical line with the lower extremity located upon the principal axis. The ray diagram above illustrates that when the object is located at a position beyond the center of curvature, the image is located at a position between the center of curvature and the focal point. Furthermore, the image is inverted, reduced in size (smaller than the object), and real. This is the type of information that we wish to obtain from a ray diagram. These characteristics of the image will be discussed in more detail in the next section of Lesson 3 .

Once the method of drawing ray diagrams is practiced a couple of times, it becomes as natural as breathing. Each diagram yields specific information about the image. The two diagrams below show how to determine image location, size, orientation and type for situations in which the object is located at the center of curvature and when the object is located between the center of curvature and the focal point. It should be noted that the process of constructing a ray diagram is the same regardless of where the object is located. While the result of the ray diagram (image location, size, orientation, and type) is different, the same two rays are always drawn. The two rules of reflection are applied in order to determine the location where all reflected rays appear to diverge from (which for real images, is also the location where the reflected rays intersect). In the three cases described above - the case of the object being located beyond C , the case of the object being located at C , and the case of the object being located between C and F - light rays are converging to a point after reflecting off the mirror. In such cases, a real image is formed. As discussed previously , a real image is formed whenever reflected light passes through the image location.

While plane mirrors always produce virtual images, concave mirrors are capable of producing both real and virtual images. As shown above, real images are produced when the object is located a distance greater than one focal length from the mirror. A virtual image is formed if the object is located less than one focal length from the concave mirror. To see why this is so, a ray diagram can be used. Ray Diagram for an Object Located at the Focal Point Thus far we have seen via ray diagrams that a real image is produced when an object is located more than one focal length from a concave mirror; and a virtual image is formed when an object is located less than one focal length from a concave mirror (i.e., in front of F). But what happens when the object is located at F? That is, what type of image is formed when the object is located exactly one focal length from a concave mirror? Of course a ray diagram is always one tool to help find the answer to such a question. However, when a ray diagram is used for this case, an immediate difficulty is encountered. The incident ray that begins from the top extremity of the object and passes through the focal point does not meet the mirror.

Thus, a different incident ray must be used in order to determine the intersection point of all reflected rays. Any incident light ray would work as long as it meets up with the mirror. Recall that the only reason that we have used the two we have is that they can be conveniently and easily drawn. The diagram below shows two incident rays and their corresponding reflected rays. For the case of the object located at the focal point (F), the light rays neither converge nor diverge after reflecting off the mirror. As shown in the diagram above, the reflected rays are traveling parallel to each other. Subsequently, the light rays will not converge on the object's side of the mirror to form a real image; nor can they be extended backwards on the opposite side of the mirror to intersect to form a virtual image. So how should the results of the ray diagram be interpreted? The answer: there is no image!! Surprisingly, when the object is located at the focal point, there is no location in space at which an observer can sight from which all the reflected rays appear to be diverging. An image is not formed when the object is located at the focal point of a concave mirror. We Would Like to Suggest ...

Why just read about it and when you could be interacting with it? Interact - that's exactly what you do when you use one of The Physics Classroom's Interactives. We would like to suggest that you combine the reading of this page with the use of our Optics Bench Interactive or our Name That Image Interactive . You can find this in the Physics Interactives section of our website. The Optics Bench Interactive provides the learner an interactive enivronment for exploring the formation of images by lenses and mirrors. The Name That Image Interactive provides learners with an intensive mental workout in recognizing the image characteristics for any given object location in front of a curved mirror. Check Your Understanding The diagram below shows two light rays emanating from the top of the object and incident towards the mirror. Describe how the reflected rays for these light rays can be drawn without actually using a protractor and the law of reflection. See Answer These two incident rays will pass through the image point for the top of the object. In fact, any light rays emanating from the top of the object will pass through the image point. Thus, merely construct a ray diagram to determine the image location; use the two rules of reflection.

Then draw the reflected rays for the two given incident rays through the same image point. Molecular Expressions: Science, Optics, and You: Light and Color - Introduction to Lenses Home Introduction to Lenses The term lens is applied to a piece of glass or transparent plastic, usually circular in shape, that has two surfaces that are ground and polished in a specific manner designed to produce either a convergence or divergence of light. The two most common types of lenses are concave and convex lenses, which are illustrated below in Figure 1. A common bi-convex lens is considered a positive lens because it causes light rays to converge, or concentrate, to form a real image. Real images can be projected onto a screen or viewed without the aid of additional lenses, but appear inverted or opposite the orientation of the object viewed. These lenses are thicker at the center than the periphery and appear to be bulging outward in a hemispherical manner with a constant curvature of radius. The bi-convex lens illustrated in Figure 1(a) has a focal point at point F with a corresponding focal length FL.

Since this convex lens is symmetrical with equal curvature angles on both sides of the lens, there is another focal point of the same length as FL on the other side of the lens, although it is not illustrated. Concave lenses, on the other hand, are considered to be negative lenses because light waves passing through them diverge, or are scattered away from, a focal point or centerline. This divergence occurs because the lens is thinner in the center and thicker on the periphery, causing light entering the lens to be refracted away from its center. The bi-concave lens illustrated in Figure 1(b) operates in a manner similar to concave mirrors, with which light waves are refracted as if they were emitted from a point behind the lens. These waves converge on a negative focal point, labeled F in Figure 2(b). Since light does not actually converge on this point, it is called a virtual focus point and the corresponding image is a virtual image. Virtual images appear erect or in the same orientation as the real object, but can only be viewed or projected with the aid of another lens. Interactive Java Tutorial Explore how lens shape affects the interaction of light with the lens.

As illustrated in Figure 1, a lens operates by refracting incoming light waves at points where they enter and exit the lens. The angle of that refraction, however, and therefore the focal length of a lens, depends upon the material of which it is composed. Materials with a high index of refraction have a shorter focal length than those with lower refractive indices (RI). For example, lenses made of synthetic polymers such as Lucite (RI = 1.47) have a lower refractive index than glass (RI = 1.51), which results in their having a slightly longer focal length. Fortunately, the refractive indices of Lucite and glass are so close together that Lucite can be used in place of glass in many lens applications, such as the popular disposable camera. As another example, a lens made of pure diamond (RI = 2.42) would have a focal length significantly less than either glass or Lucite, though the cost of designing such a lens would be prohibitive. Lenses of various shapes, sizes, and materials enjoy a wide variety of usage.

For instance, single lenses able to form real images are found in tools used for simple magnification, such as magnifying glasses, eyeglasses, single-lens cameras, viewfinders, and contact lenses. More complex devices, such as compound microscopes, telescopes, and binoculars, use a combination of lenses in order to enhance magnification and other desirable optical properties. However, these instruments are commonly plagued by lens errors that distort images by a variety of mechanisms associated with aberrations, or defects, resulting from the spherical geometry of lens surfaces. There are several types of lens errors, but the general effect of optical aberrations in a microscope is the appearance of faults in the tiny features and details of an image that is being observed. Thus, aberration is one of many factors that should be considered when deciding what kind of lens to use. Most lenses are classified according to their two principal surfaces and curvature patterns, since the type of refraction that occurs when light travels through a lens is dependent upon the geometry of that lens. Basic lens groups are typically divided into two sub-categories, the convergent lenses and the divergent lenses. Each category contains several different lens types, which are addressed individually below.

The Bi-Convex Lens - The simplest magnifying lens is the bi-convex (sometimes called the double-concave) convergent lens that condenses light rays into a focal point, as illustrated in Figure 1(a). The focal length of a bi-convex lens, also featured as Figure 2(a), is dependent upon the curvature angle of its faces. Higher angles of curvature result in shorter focal lengths due to the fact that light waves are refracted at a greater angle with respect to the centerline of the lens. The symmetric nature of bi-convex lenses minimizes spherical aberration in applications where the image and object are at symmetrical distances. These lenses are typically used for focusing and image magnification. The Bi-Concave Lens - Concave lenses, like the one illustrated in Figure 2(d), are primarily used for diverging light and image reduction, as well as increasing system focal lengths and collimating converging light beams. The bi-concave (sometimes called the double-concave) lens refracts parallel input rays so that they diverge away from the optical axis on the output side of the lens, but form a negative focal point in front of the lens, as illustrated in Figure 1(b).

While the output rays do not actually cross to form a focal point, they do appear to be diverging from a virtual image located on the object side of the lens. Bi-concave lenses are often coupled with other lenses in order to reduce the focal lengths of optical systems. The Plano-Convex Lens - Figure 2(b) and Figure 3 depict typical plano-convex lenses that have one positive hemispherical side and one flat side. Plano-convex lenses are convergent, focusing parallel rays of light to a positive focal point, as illustrated in Figure 3. Thus, these lenses form real images, which can be projected or manipulated by spatial filters. The asymmetry of plano-convex lenses minimizes spherical aberration in applications where the object and image lie at unequal distances from the lens. When the curved surface of the lens is oriented toward the object, the sharpest possible focus is achieved. Plano-convex lenses are useful for collimating diverging beams of light and for applying focus to an optical system. The Concavo-Convex Lens - The third type of convergent lens is the concavo-convex lens, which is depicted in Figure 2(c) and Figure 4.

More commonly known as the positive (converging) meniscus lens, this lens also has an asymmetric structure. One of its faces is in a convex hemispherical shape, while the other is slightly concave. Meniscus lenses are used most often in conjunction with another lens to produce an optical system of a longer or shorter focal length than the original lens. For instance, a positive meniscus lens can be placed after a plano-convex lens to shorten its focal length without decreasing the performance of the optical system. Positive meniscus lenses have a greater curvature radius on the concave side of the lens than on the convex side, which enables the formation of a real image. The Plano-Concave Lens - The plano-concave lens, illustrated in Figure 2(e) and Figure 5, is a divergent lens that has a negative focal point and produces a virtual image. When a collimated light beam is incident on the curved surface of a plano-concave lens, the exit side forms a divergent beam. This beam appears to emerge from a smaller virtual point source than if the plane surface had faced the collimated beam.

Plano-concave lenses are used to expand light beams or to increase focal lengths in existing optical systems. The Convexo-Concave Lens - This lens is commonly referred to as a negative (divergent) meniscus lens, since its concave surface has a lower curvature radius than its convex surface, as illustrated in Figure 2(f) and in Figure 6. This type of lens can be used to reduce or eliminate spherical aberration in optical systems with which the lens is coupled and can be combined with other lenses to produce increased resolution capabilities. Contributing Authors Mortimer Abramowitz - Olympus America, Inc., Two Corporate Center Drive., Melville, New York, 11747. Shannon H. Neaves and Michael W. Davidson - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310. LENSES LENSES FIND OUT MORE When you look through a magnifying glass, or take a picture with a camera, you are using a lens. A lens is a polished piece of glass or transparent plastic with curved surfaces. There are two main shapes of lenses, CONVEX and CONCAVE .

WHAT DOES A LENS DO? A lens changes the direction of light waves by refraction. It may form an image of a scene or an object. The image might be smaller (as in a camera), or larger (as in a microscope). Because a lens is curved, light rays strike different parts of its surface and are bent by different amounts. Depending on the lens shape, a beam of light either diverges (spreads out) or converges (concentrates). WHAT IS THE DIFFERENCE BETWEEN A MICROSCOPE AND A TELESCOPE? A microscope makes a tiny, nearby object look much bigger. A telescope makes a large, distant object or scene appear much closer and brighter. In both instruments, light from the object passes through two or more lenses to form an image. The shapes of the lenses and the distances between them alter the image that is produced. CONVEX LENS This type of lens is thicker in the center than at the edge. Parallel rays of light entering it on one side will converge (meet) at a particular spot on the other side of the lens. Magnifying glasses and microscopes use convex lenses. HOW DOES A MAGNIFYING GLASS WORK? A magnifying glass makes an object look bigger.

Holding it close to an object makes a virtual image of the object form on the same side of the glass as the object. When you look through the magnifying glass, this virtual object seems to be larger than the real one. The thicker the lens, the larger the virtual image. Diverging (spreading) light rays are made parallel by the first convex lens. The second convex lens angles the parallel rays so that they converge—meet or focus—at a certain point, called the focal point. CONCAVE LENS A concave lens is thinner at the center than at the edge. Parallel light rays passing into one side of the lens diverge (spread out) as they emerge from the other side. HOW DO CONCAVE LENSES HELP YOU SEE? If you are nearsighted, your eye lens focuses a scene just in front of the retina in your eye and the image you see is blurred. A concave lens spreads out the light rays before they enter the eye, so that they are focused on the retina and the image is sharp. Diverging light rays are made parallel by a convex lens. But when the parallel light rays pass through a concave lens, they diverge (spread out) again.

FIND OUT MORE Definition of Concave lens | define Concave lens - physics dictionary Online - Concave Lens Definition of Concave Lens A lens which is thicker at the edges and thinner at the centre is known as concave lens. n. This type of lens bends the rays of light outwards.. More About Concave Lens Concave lens is also known as diverging lens as it diverges the light rays. It is made up of number of prisms with the base of each prism away from the centre of the lens. The central part of the lens is a simple parallel sided glass. The parallel sided glass slab allows the light rays to pass through it without any deviation. The upper part of the lens deviates the light rays upwards and lower part deviates the rays downwards. The following are the different types of concave lenses: 1. Double concave Diverging Lenses - Ray Diagrams Refraction and the Ray Model of Light - Lesson 5 - Image Formation by Lenses Diverging Lenses - Ray Diagrams Earlier in Lesson 5 , we learned how light is refracted by double concave lens in a manner that a virtual image is formed.

We also learned about three simple rules of refraction for double concave lenses : Any incident ray traveling parallel to the principal axis of a diverging lens will refract through the lens and travel in line with the focal point (i.e., in a direction such that its extension will pass through the focal point). Any incident ray traveling towards the focal point on the way to the lens will refract through the lens and travel parallel to the principal axis. An incident ray that passes through the center of the lens will in effect continue in the same direction that it had when it entered the lens. These three rules will be used to construct ray diagrams. A ray diagram is a tool used to determine the location, size, orientation, and type of image formed by a lens. Ray diagrams for double convex lenses were drawn in a previous part of Lesson 5. In this lesson, we will see a similar method for constructing ray diagrams for double concave lenses. Step-by-Step Method for Drawing Ray Diagrams The method of drawing ray diagrams for a double concave lens is described below. 1. Pick a point on the top of the object and draw three incident rays traveling towards the lens.

Using a straight edge, accurately draw one ray so that it travels towards the focal point on the opposite side of the lens; this ray will strike the lens before reaching the focal point; stop the ray at the point of incidence with the lens. Draw the second ray such that it travels exactly parallel to the principal axis. Draw the third ray to the exact center of the lens. Place arrowheads upon the rays to indicate their direction of travel. 2. Once these incident rays strike the lens, refract them according to the three rules of refraction for double concave lenses. The ray that travels towards the focal point will refract through the lens and travel parallel to the principal axis. Use a straight edge to accurately draw its path. The ray that traveled parallel to the principal axis on the way to the lens will refract and travel in a direction such that its extension passes through the focal point on the object's side of the lens. Align a straight edge with the point of incidence and the focal point, and draw the second refracted ray. The ray that traveled to the exact center of the lens will continue to travel in the same direction. Place arrowheads upon the rays to indicate their direction of travel. The three rays should be diverging upon refraction.

3. Locate and mark the image of the top of the object. The image point of the top of the object is the point where the three refracted rays intersect. Since the three refracted rays are diverging, they must be extended behind the lens in order to intersect. Using a straight edge, extend each of the rays using dashed lines. Draw the extensions until they intersect. All three extensions should intersect at the same location. The point of intersection is the image point of the top of the object. The three refracted rays would appear to diverge from this point. This is merely the point where all light from the top of the object would appear to diverge from after refracting through the double concave lens. Of course, the rest of the object has an image as well and it can be found by applying the same three steps to another chosen point. See note below . 4. Repeat the process for the bottom of the object. The goal of a ray diagram is to determine the location, size, orientation, and type of image that is formed by the double concave lens. Typically, this requires determining where the image of the upper and lower extreme of the object is located and then tracing the entire image.

After completing the first three steps, only the image location of the top extreme of the object has been found. Thus, the process must be repeated for the point on the bottom of the object. If the bottom of the object lies upon the principal axis (as it does in this example), then the image of this point will also lie upon the principal axis and be the same distance from the lens as the image of the top of the object. At this point the complete image can be filled in. Some students have difficulty understanding how the entire image of an object can be deduced once a single point on the image has been determined. If the object is merely a vertical object (such as the arrow object used in the example below), then the process is easy. The image is merely a vertical line. This is illustrated in the diagram below. In theory, it would be necessary to pick each point on the object and draw a separate ray diagram to determine the location of the image of that point. That would require a lot of ray diagrams as illustrated in the diagram below. Fortunately, a shortcut exists. If the object is a vertical line, then the image is also a vertical line.

For our purposes, we will only deal with the simpler situations in which the object is a vertical line that has its bottom located upon the principal axis. For such simplified situations, the image is a vertical line with the lower extremity located upon the principal axis. The ray diagram above illustrates that the image of an object in front of a double concave lens will be located at a position behind the double concave lens. Furthermore, the image will be upright, reduced in size (smaller than the object), and virtual. This is the type of information that we wish to obtain from a ray diagram. The characteristics of this image will be discussed in more detail in the next section of Lesson 5 . Your Turn to Practice Once the method of drawing ray diagrams is practiced a couple of times, it becomes as natural as breathing. Each diagram yields specific information about the image. It is suggested that you take a few moments to practice a few ray diagrams on your own and to describe the characteristics of the resulting image. The diagrams below provide the setup; you must merely draw the rays and identify the image. If necessary, refer to the method described above . We Would Like to Suggest ... Why just read about it and when you could be interacting with it?

Interact - that's exactly what you do when you use one of The Physics Classroom's Interactives. We would like to suggest that you combine the reading of this page with the use of our Optics Bench Interactive . You can find this in the Physics Interactives section of our website. The Optics Bench Interactive provides the learner an interactive enivronment for exploring the formation of images by lenses and mirrors. Its like having a complete optics toolkit on your screen. Optics For Kids - The Optical Society: Exploring the Science of Light Lenses and Geometrical Optics The Focal Length We use lenses and mirrors everyday but sometimes don't really understand how and why they do what they do. In this section of the Readings, we'll learn a little more about how light interacts with such things as lenses and how this interaction can help us. Most optical elements (mirrors, lenses) can be characterized by basically one quantity: their focal length. To understand focal length, we need to know something about the focal point. In the image above, note how the light rays, after they pass through the lens, converge on a single point. Below is a schematic drawing of the above situation.

The single point to which the light rays are converging is called the focal point. The distance, f, from the lens to the focal point is the focal length. Each lens and mirror has its own focal length, which is its defining characteristic. Note, however, that in showing the focal length of the lens above, we used light rays that were all parallel as they came to the lens. This isn't always the case: we can have light rays incident at different angles. In the case above, the focal point is farther from the lens, because the incident rays were diverging as they came to the lens. What would happen if the rays were already converging as they hit the lens? Where would we find the focal length in that case? So when we discuss the "focal length" of a certain lens or mirror, we are usually referring to the focal length you get when a distant object's light rays (parallel light) are incident on the lens or mirror. Real vs. Virtual The lenses and mirrors that we are using in this module come in two basic flavors: convex and concave. The lenses A and B in your Optics Kit are called double convex lenses and have positive focal lengths.

They have sides that bulge outwards and, as we saw above, converge light to a focal point. Lens C in your Kit is called a double concave lens and has a negative focal length. The concave lens has sides that bulge inward and diverge light. What does it mean for a lens to have a negative or positive focal length? A positive focal length means that the focal point of the lens is on the other side of the lens from where the object is placed. On the other hand, a negative focal length means that the focal point is on the same side of the lens as where the object is placed. This terminology is just a useful convention that allow physicists and engineers to characterize lenses and mirrors; it has no real physical meaning. But how can we have an image on the same side of the lens as the object? In an earlier activity, you tried to image (bring to a focus) the room lights with your various lenses. Did you get an image of the lights with your concave lens (Lens C)? Most likely not, since the concave lens, as we have seen, diverges light and can't bring light beams to a focus.

The image, if there was one, would have been on the same side of the lens as the source (the light). This kind of image on the same side as the source is called a virtual image . It's an image that isn't really there; the focal point in the drawing above is just the point where the rays would converge if they could. We can't focus the beams onto a piece of paper, for instance like you tried earlier. The strange thing about a virtual image, however, is that we can see it! So what kind of image does a convex lens make? The drawing below shows us that a convex (positive) lens forms images on the side of the lens opposite the source. Since we can form an image on a piece of paper, we call this kind of image a real image. As you've probably guessed, we can also see real images. The mirror tells all Real and virtual images are not relegated to the domain of just the lenses -- if you want to see another virtual image look in your bathroom mirror. Or in the curved mirror on the passenger side of your car.

Virtual images in a mirror form on the image side of a mirror, unlike that of lenses, in which the virtual image forms on the object side of the lens. Again, however, the virtual image is not a true image, in that it cannot be projected onto a screen. This is because the light rays reflecting off a plane mirror never converge, the major criterion for creating a real image. Likewise, light bouncing off a convex mirror never converge, thus these mirrors create virtual images. The dotted lines represent the extension of the reflected light rays if they could go through the mirror. Only concave mirrors can create real images. When light hits the surface of a concave mirror, an individual light ray is reflected at an acute angle and all the light converges at a point on the object side of the mirror. Most real images are seen inverted (upside-down) while virtual images are seen upright. Look in both faces of a well-polished spoon. One surface is a convex mirror, the other is a concave mirror: on which side is your image inverted? Ray Tracing We've seen how we can find the focal length of various types of lenses, and what the difference is between a real and a virtual image.

Now we need to bring these concepts together so we can use them to our advantage. Let's pretend for a moment that we live in a world in which the optometrists or opthamologists won't make our eyeglasses or contact lenses. If you had the raw materials and knew the prescription of your eyes (the eye doctors will at least do that service), how could you find the right lenses to make? We could make some lenses and test them until we found the right ones, but this might make our eyes pretty tired and would take a long time. If we knew the focal length of various lenses, we would be able to use a much more powerful technique to make our glasses. Ray tracing allows us to "see" how light is going to behave when we have lenses and mirrors in the path of the light. If we know where the focal point of each lens and mirror is, we can figure out where the image of a certain object will be formed. This will tell us where the image will fall on our retina so we can see it. The idea is to draw light rays emanating from the object through the optical system (lenses & mirrors).

The diagram below shows how much of the light from the light source (a candle) passes through the lens and is imaged on the other side (notice that the ray that started at the top of the candle ends up below the ray that started at the bottom of the flame: the image is upside down). Since there are an uncountable number of light rays (shaded area above) passing through the lens(es), it would be unreasonable to draw them all. Usually, we need draw only 2 or 3 rays from a point on the light source to represent all the rays coming from that point. If we know the focal length of each of the lenses and/or mirrors, our 3 rays will show us where the image of a point from the source (or object) will be located.

In the diagram above, I chose "special" rays to locate the image: the ray (1) passing through the center of the lens will always travel in a straight line without refracting; the ray (2) coming straight in from the candle top (parallel to the optical axis) is bent so it passes through the focal point on the other side of the lens; and the ray (3) passing through the focal point on the object (the left) side of the lens will be refracted so the light will exit the lens travelling parallel to the optical axis. A very similar diagram could be drawn for the light rays coming from the bottom of the candle, or from any other point on the candle. With this technique of tracing various rays from a light source, we can tell where an image will form and how it will be oriented: inverted or upright. Want to try activities highlighting these principles? Click on the name of this activity to find an easy, hands-on experiment: Differences between lenses and mirrors Light reflects from a mirror. Light goes through, and is refracted by, a lens. Lenses have two focal points, one on either side of the lens. A concave mirror converges light to a focal point.

For lenses, light converges to a point for a convex lens. A convex mirror diverges light, as does a concave lens. Any lens that is thicker in the center than the ends is a convex lens. Any lens thicker at the ends than in the center is a concave lens. Similarities between lenses and mirrors The equations we used for mirrors all work for lenses. A convex lens acts a lot like a concave mirror. Both converge parallel rays to a focal point, have positive focal lengths, and form images with similar characteristics. A concave lens acts a lot like a convex mirror. Both diverge parallel rays away from a focal point, have negative focal lengths, and form only virtual, smaller images. The sign convention is just a little different. Because the light goes through the lens positive image distances (and real images) are on the opposite side of the lens from the object. Negative image distances are for virtual images, again, but those are on the same side of the lens as the object. Converging lens: Convex Mirror: Ray Diagram for a Convex Lens Once again, a ray diagram can help us understand what a lens does.

Send rays out from the object, refract them through the lens, and see where they go. The image is where the rays intersect. Rays that are easy to draw include: The parallel ray goes from the tip of the object horizontally to the lens. It refracts through the lens and passes through the focal point on the far side of the lens. The chief ray is a straight line starting from the tip of the object and passing through the center of the lens. As long as the lens is thin we can assume the ray passes straight through. The focal ray is a mirror image of the parallel ray. It goes from the tip of the object through the focal point on the object side of the lens, and emerges from the lens going parallel to the principal axis. Image Characteristics for a Convex Lens The table shows what happens to the image as an object is brought from infinity toward a convex lens. Object Position Moving from F toward lens Moving from -infinity toward lens Decreasing in size, virtual, upright, larger than the object As long as the image as real the ray diagram is reversible. An object at point A creates an image at point B, while an object at point B creates an image at point A.

Ray Diagram for a Concave Lens What happens with a concave lens? The parallel ray goes from the tip of the object horizontally to the lens. It refracts through the lens and diverges away from the principal axis going directly away from the focal point on the object side of the lens. The chief ray is a straight line starting from the tip of the object and passing through the center of the lens. As long as the lens is thin we can assume the ray passes straight through. The focal ray leaves the tip of the object heading toward the focal point on the far side of the lens. It is re-directed by the lens to go parallel to the principal axis. Moving an object from infinity toward a concave lens gives an image that moves from the focal point toward the lens, growing from a point to almost as large as the object. The image is virtual, upright, and smaller than the object. Molecular Expressions: Physics of Light and Color - Image Formation with Diverging Lenses: Interactive Java Tutorial Interactive Java Tutorials Image Formation with Diverging Lenses Negative lenses diverge parallel incident light rays and form a virtual image by extending traces of the light rays passing through the lens to a focal point behind the lens.

In general, these lenses have at least one concave surface and are thinner in the center than at the edges. This interactive tutorial utilizes ray traces to explore how images are formed by the three primary types of diverging lenses, and the relationship between the object and the image formed by the lens as a function of distance between the object and the focal points. The tutorial initializes with an object (represented by the larger vertical gray arrow on the far left-hand side of the lens) positioned approximately twice the distance of the focal length away from a simple thin bi-concave lens. Ray traces emanating from the point of the object arrow (Object) pass through various points on the lens and are diverged away from ray extensions traced back to the focal point (F). Three of the rays are illustrated in red: the Principal Ray, which passes through the center of the lens, and two additional characteristic rays. One of the characteristic rays travels towards the lens rear focal point (F'), but is diverted in a direction parallel to the Optical Axis after passing through the lens. The other characteristic ray travels toward the lens parallel to the optical axis and diverges sharply away from the axis after passing through the lens.

Extensions drawn from any two of these three rays can be utilized to determine the size and placement of the Virtual Image formed by the lens. In order to operate the tutorial, use the Object Position slider to translate the object arrow back and forth along the optical axis of the lens. As the object is moved closer to the lens, the virtual image size increases and also moves closer to the lens. In a similar manner, as the object is moved away from the lens, the virtual image moves away from the lens and grows smaller. The distance between the lens and the object (Object Distance, (p)) and image (Image Distance, (q)) are continuously updated in the lower left-hand corner of the tutorial window. The bi-concave lens can be changed to either a Negative Meniscus or Plano-Concave element by selecting the appropriate choice using the pull-down menu. When a negative lens is placed between an object and the eye, it does not form a real image, but reduces (or demagnifies) the apparent size of the object by forming a virtual image. The distinction between a real and a virtual image is an important concept when imaging specimens through a lens or mirror system, regardless of whether the system consists of a single or multiple components.

In general, images are defined by the regions where light rays (and their extensions) become convergent as the result of refraction by a lens or reflection by a mirror. In cases where the light rays intersect at a focal point, the image is real and can be viewed on a screen, recorded on film, or projected onto the surface of a sensor such as a CCD or CMOS placed in the image plane. When the light rays diverge, but project imaginary extensions that converge to a focal point, the image is virtual and cannot be viewed on a screen or recorded on film. In order to be visualized, a real image must be formed on the retina of the eye. When viewing specimens through the eyepieces of a microscope, a real image is formed on the retina, but it is actually perceived by the observer to exist as a virtual image located approximately 10 inches (25 centimeters) in front of the eye.

Negative lens elements are the bi-concave (Figure 1(a)), plano-concave (Figure 1(b); with a single planar surface), and concave-meniscus (also termed a negative meniscus lens; Figure 1(c)), which also has concave and convex surfaces, but with the center of the lens being thinner than the edges. For both positive and negative meniscus lenses, the distances between the surfaces and their focal planes are unequal, but their focal lengths are equal. The line passing through the center of the lens curved surfaces in Figure 1(a) is known as the optical axis of the lens. Simple lenses having a symmetrical shape (bi-convex or bi-concave) have principal planes that are equally spaced with respect to each other and the lens surfaces. The lack of symmetry in other lenses, such as the meniscus lenses and the plano negative and positive lenses, causes the locations of the principal planes to vary according to lens geometry. Plano-convex and plano-concave lenses have one principal plane that intersects the optical axis, at the edge of the curved surface, and the other plane buried inside the glass. The principal planes for meniscus lenses lie outside the lens surfaces.

Bi-concave lenses (Figure 1(a)) are primarily utilized for diverging light beams and image size reduction, as well as increasing optical system focal lengths and collimating converging light beams. Often termed the double-concave lens, this optical element refracts parallel input rays so that they diverge away from the optical axis on the output side of the lens, forming a negative focal point in front of the lens. Although the output light rays do not actually unite to form a focal point, they do appear to be diverging from a virtual image located on the object side of the lens. Bi-concave lenses can be coupled to other lenses to reduce optical system focal lengths. The plano-concave lens illustrated in Figure 1(b) is a divergent element that has a negative focal point and produces a virtual image. When a collimated light beam is incident on the curved surface of a plano-concave lens element, the exit side will form a divergent beam. This beam will appear to emerge from a smaller virtual point source than if the planar lens surface had faced the collimated light beam.

Plano-concave lenses, which feature minimal spherical aberration when the concave surface is facing the longest conjugate distance, are employed to expand light beams or to increase focal lengths in existing optical systems. Also referred to as a convexo-concave lens, the negative (divergent) meniscus lens (Figure 1(c)) can be designed to reduce or eliminate additional spherical aberration or coma in optical systems to which the lens is coupled. Meniscus lenses (both positive and negative) are often employed to shorten the focal length of a doublet (two lens elements cemented together) or a plano-convex lens operating at an infinite conjugate ratio (illuminated by parallel light rays). The desired focal length of the final system determines the particular dimensions and character of the meniscus lens that should be added. Plano-convex/meniscus lens combinations display up to four times greater resolution than a plano-convex lens working alone. Contributing Authors Matthew J. Parry-Hill, Robert T. Sutter and Michael W.

Davidson - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310. Curved Mirrors - Physics | Socratic Curved Mirrors Tip: This isn't the place to ask a question because the teacher can't reply. Post There are more differences than similarities. Explanation: DIFFERENCES: 1. Convex mirror is formed by the surface of a sphere which is facing away from the centre, where as concave is formed by the one facing towards the centre. 2. Convex mirrors(vex) diverges a parallel beam of light.But concave mirrors(cave) converges a parallel beam of light. 3. The above point implies that vex has focal length +ve according to convention, -ve focal length for cave. 4. vex can only form virtual images whereas cave can form both virtual and real images. 5. All these differences mean they have different applications. SIMILARITIES : 1. Both are part of a sphere. 2. The mirror formula can be applied for both.

#1/v +1/u = 1/f, " "# - focal length (sign conventions have to be used while using these eqns.) 3. Image formation in both are based on the application of Laws of reflection at small scale i.e by taking the line joining a point on the mirror to the centre as the normal. Sudhish P. · 4 · 6 comments · Oct 12 2015 In optics, a focal point is a point at which rays or waves meet after reflection or refraction, or the point from which diverging rays or waves appear to proceed. Converging (convex) and diverging (concave) lenses all have two focal points--one on each side of the lens. Curved mirrors generally have just one focal point--in front for the case of concave mirrors, and behind the mirror in the case of convex mirrors. When parallel rays enter a convex lens parallel to its principal axis, they will be gathered at its focal point. Conversely, light originating from a point source located at the focal point of a convex lens will exit the lens in parallel rays.

Parallel rays of light that strike a concave (parabolic) mirror will reflect off so as to be gathered at the focal point of the mirror. Conversely, light originating from a point source located at the focal point of the concave mirror will reflect off the mirror in parallel rays. That is how search lights are set up (also the bat signal). Not that the focal point is in general NOT the image location when an image is formed by a curved mirror or lens. Scholars J. · 1 · 8 comments · May 21 2014 Source A convex lens has two focal points - one on each side. They are equal distances from the lens. The lens does not have to have the same curvature on both sides for this to be true, and it doesn't depend on the direction the light takes entering the lens. It is the combined curvature that determines the focal point. Ashley · · 9 comments · Jul 22 2014 Examples of a curved mirror would be the rear view mirrors on the side of a car, inside of a telescope, in shopping malls to see around corners, or in fun houses to give your body different shapes.

Here is an example of a curved mirror used to see around corners: Here is a mirror used in grocery stores for workers to see customers: These mirrors have many uses, such as being able to see around corners, using multiple mirrors together to gain an image in a telescope, and in cars to make rear view mirrors more useful. Spencer W. · · 7 comments · Aug 27 2014

Question: What diverges rays of light, if it is concave?
Answer: Lens