Option C - Imaging (Optics)

Option C is not information that we learned/will learn in class. In paper 3, we are given Option A, B, C, D, or E to choose from, and you only choose one, thus many of us chose to study Option C as a substitute of doing Option A on the exam, since Option C is simply optics that is much easier to understand.

It is completely optional to study this option. You may stick with Option A (Relativity) if you wish. The information on this page is for those who wish to study it.

So far, only the textbook has been used to explain this lesson.

## C-1 Introduction to Imaging

###  **Mirrors**

#### **Concave (converging) Mirrors**

* Mirrors that curve inwards, towards the light rays.
* Example: http://sciencelearn.org.nz/var/sciencelearn/storage/images/contexts/light-and-sight/sci-media/images/concave-mirror/685441-1-eng-NZ/Concave-mirror.jpg

#### **Convex (diverging) Mirrors**

* Mirrors that curve outwards, away from the light rays
* Example: http://sciencelearn.org.nz/var/sciencelearn/storage/images/contexts/light-and-sight/sci-media/images/convex-mirror/685505-1-eng-NZ/Convex-mirror.jpg

#### **Principal Axis**

* Is the line that goes through the center of the mirror surface at 90o

#### **Principal Focus (Focal Point)**

* When the light rays are close and parallel to the principal axis, and are indicent on the concave mirror, then they all reflect through a point known as the **Principal Focus**
* Usually coined as **Point F**
* The Concave Mirror example illustrates this.
* The Convex Mirror has an imaginary focal point, which exists on the other side of the mirror. Again, its example illustrates this.

#### **Law of Reflection**

* States that the angle of incidence (i) at the mirror is equal to the angle of reflection (r).

#### **Curved Mirror Ray Diagrams**

* Mirrors reflect an image. Some images may seem closer/further than its actual distance from the mirror. Ray diagrams determined exactly where the image seem to be in the mirror.
* This method only works for spherically curve mirrors, and if the rays are close to the **Principal Axis**. Other mirrors will have different ray diagrams.

**Drawing Ray Diagrams**

* You must know where the **Principal Focus** is. Point F represents the **Principal Focus**. Point C is simply twice the distance of the Focal Length (the length from the mirror to the **Principal Focus**)
* Concave Example: http://getphysicshelp.weebly.com/uploads/1/8/4/4/18441397/225467811.JPG
* Convex Example: http://images.tutorvista.com/cms/images/38/ray-diagram-convex-mirror.JPG

**Instructions for Concave Mirrors (Use the example as guidance)**

1. Draw an arrow that represents the object.
2. Draw a line (starting at the tip of the arrow) that heads towards the mirror initially parallel to the **Principal Axis**, then reflect the ray directly THROUGH the **Principal Focus.**
3. Draw a second line (starting at the tip of the arrow) that goes through the **Principal Focus**, then reflect the ray to be parallel to the **Principal Axis.**
4. Draw another arrow that points from the **Principal Axis** to the intersection of the two lines. This line must be perpendicular to the **Principal Axis**, just like step 1.
5. Label arrows on the lines to show their directions.

The general rule is that if the object is:

* beyond point C, the image is smaller and upside down (since it appears on the other side of the **Principal Axis**)
* At point C, the image is the same size as the object and upside down.
* Between point C and point F, the image is larger and upside down.
* At Point F, no image is formed since the rays do not intersect in any way.
* Beyond point F gets a little trickey:

https://dj1hlxw0wr920.cloudfront.net/userfiles/wyzfiles/c77bc409-8651-4527-a1d1-64b2728163c0.png

It follows the same concepts, but produces a virtual image that is inside of the mirror instead. This image will appear larger, and straight up (since the image appears on the same side of the **Principal Axis**). This virtual image is no different than the real images.

**Instructions for Convex Mirrors (Use the example as guidance)**

1. Draw an arrow that represents the object.
2. Draw a line (starting at the tip of the arrow) that heads towards the mirror initially parallel to the **Principal Axis**, then reflect the ray directly AWAY from the **Principal Focus**.
3. Draw dotted lines to connect the **Principal Focus** the previous drawn line.
4. Draw a line (starting at the tip of the arrow) that goes through the center of curvature (point C). As the line goes through the mirror, change the line into a dotted line when it is behind the mirror.
5. Draw another arrow that that points from the **Principal Axis** to the intersection of the two lines. This line must be perpendicular to the **Principal Axis**, just like step 1.
6. Draw arrows on the lines to show their directions.

Unlike the concave mirror, the image is always virtual, smaller, and upright.

#### **Magnification**

Magnification: m = height of image/height of object = hi / ho

#### **Spherical Aberrations (distortions)**

* Remember that the ray diagrams only work for rays that are close to the **Principal Axis**. So what if they are not close to that axis?
* If there were many parallel rays hitting all of the mirror, it would look like this:

https://upload.wikimedia.org/wikipedia/commons/1/1a/Circle\_caustic.png

* This is known as the **Caustic Curve**
* This apparently can be a problem (maybe its ugly?), so a parabolic mirror can be used instead.

* It is often used to collect all the light into one spot.

### **Lenses**

* We assume that lens thickness does not affect anything
* **Optical Center** of the lens is the exact center in the lens where light is not deviated.

#### **Converging Lenses**

* Converging lens makes rays come together
* Much like the concave mirror, the concepts follow.
* Example: http://www.district196.org/avhs/dept/science/physics/physicsweb04/AVHSPhysics/images/lensdiag4.GIF

#### **Converging lens diagram**

1. Draw the arrow for the object
2. Draw a line heading towards the lens initially parallel to the **Principal Axis**, then refract it through the focal point on the other side of the lens.
3. Draw a line through the **Optical Centre** of the lens, and it should intercept with the previous line.
4. (This step only for if the object is beyond point F) The lines will not intercept if so, thus the lines must be traced backwards with dotted lines to form a virtual image. Example: http://www.physicsclassroom.com/Class/refrn/u14l5da7.gif
5. Draw another arrow to represent the image.

The general rule is that if the object is (this is exact same as concave mirror):

* beyond point C, the image is smaller and upside down (since it appears on the other side of the **Principal Axis**)
* At point C, the image is the same size as the object and upside down.
* Between point C and point F, the image is larger and upside down.
* At Point F, no image is formed since the rays do not intersect in any way.
* Beyond point F produces a virtual image: larger and upright.

Converging lens are useful for magnifying glasses, since the image is enlarged when the object is closer than focal point.

#### **Diverging Lenses**

* Lens that directs rays AWAY from each other
* The final image is ALWAY virtual, upright, and smaller than the object.
* Example: http://www.physics.mun.ca/~jjerrett/lenses/Diverge.gif

#### **Diverging lens diagram**

1. Draw the arrow for the object
2. Draw a line towards the lens parallel to the **Principal Axis**, then refract it directly AWAY from the focal point.
3. Draw dotted lines that connects the focal point and the previous line.
4. Draw a line (from the object) through the **Optical Center**
5. Draw an arrow (for the image) that points towards the intersection of the lines

#### **The Lens Equation**

##### Curvature of lens

1/f = 1/u + 1/v

* v = distance between lens and image

* u = distance between lens and object
* f = distance between lens and focal point

There must be things to consider when using this formula:

* Real objects and images are treated as positive
* Virtual objects and images are treated as negative
* The focal length of a converging lens is positive
* The focal length of a diverging lens is negative

##### Power

Ability of lens to add/subtract curvature (the u and v) is determined by this equation:

P (in diopter) = 1/f -> f in meters

* The smaller focal length, the greater the power.
* A converging lens would have a positive power (positive focal length), thus known as 'positive lens'
* A diverging lens would have a negative power (negative focal length), thus known as 'negative lens'

##### Magnification

m = height of image/height of object

m = v/u

m = Xi / Xo Where X is the angle made between the intersections made by the object (Xo) and the image (Xi).

### **The Simple Magnifying Glass**

* Fun Fact: eyes have lens too! The eye can bend the lens to change its focal point.
* However, if an object that you look at is closer than 25cm away from your eye, it places strain on your eye.
* They use some other goofy formula when you try to use the magnifying glass

#### **The not so simple magnifying glass formulas**

##### Magnification without strain

m = D/f

where D = **near point**, which is the closest distance the eye can focus without putting a strain on the eye. Usually at 25cm but can vary greatly from individuals.

f = the focal length of the lens. This is the new "near point" after putting the lens on.

##### Magnification with strain

This is when you hold the object past the focal length (and thus past the new near point) of the lens.

m = D/f + 1

They used some next level equation without explanation to get to here. So just remember that if the object is closer than focal length, add one. If not, don't add one.

#### **Spherical and Chromatic Aberrations (distortions)**

Chromatic:

Colours screw up lenses because colours have different wavelengths, thus forming different focal points for different colour.

This is known as **Chromatic aberration** and the intersection of green coloured rays would show a point known as **circle of least confusion**. I didn't make these names up.

To make sure this mess doesn't happen, they use something called a **doublet lens** where you put a diverging lens at the end of the converging lens, and the rays almost all go to one spot

Spherical:

Like mirrors, lens suffer from Spherical Aberrations and weird patterns appear.

Easiest way to cure this is to cut the diameter of the lens by putting an obstacle with a hole cut in the center over the lens.

However, this will result in lower amount of light going through.

## C-2 Imaging Instrumentation

Now we finished the easy stuff, we go back to the actual grade 11 physics.

## Summarization of formulas

### Other Formula

Curvature of lenses: 1/f = 1/u + 1/v

Power of a single lens: P (in diopter) = 1/f -> f in meters

m = height of image/height of object

### Magnfication

Magnification of mirrors: m = height of image/height of object = hi / ho

m = Xi / Xo Where X is the angle made between the intersections made by the object (Xo) and the image (Xi).

Angular Magnification

Lens: m = height of image/height of object = hi / ho

Lens: m = v/u

Magnifying glass: m = D/f

For magnifying glass when object is closer than focal point: M = D/f + 1

For telescopes (2 lenses): M = fo/fe