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Oliphant W17 PH106 23:1-3

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Richard Datwyler

on 23 February 2018

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Transcript of Oliphant W17 PH106 23:1-3

Light:
Geometric
Optics
Two mirrors meet at 135 degrees. If light rays strike one mirror at 40 degrees at what angle do they leave the second mirror?
40
?
135
5
If you look at yourself in a shiny Christmas tree ball with a diameter of 9.0 cm when your face is 30.0 cm away from it, where is your image? Is it real or virtual? Is it upright or inverted?
2.09 cm behind
virtual
upright

A mirror at an amusement park shows an upright image of any person who stands 1.4 m in front of it. If the image is four times the person's height, what is the radius of curvature?
3.73 m
Two parallel plane mirror face each other 3.5 m apart. If you stand 1.5 m from one mirror, facing the closer mirror:
a) how far away from you are the first 3 images that you see?
b) what is the orientation of these images?
If you stand 1.5 m in front of a full length mirror, and your eyes are 1.25 m above your toes, how far is it from your eyes, to the image of your toes in the mirror?
Show by ray diagrams where a 4 cm tall image will form when placed 25 cm in front of a Concave mirror with a focal length of 20 cm?
Repeat but with a radius of 20 cm?

1.5
3
7
10
14
3.5
face
hair
face
hair
1.5
1.25
1.5
3.25 m
A concave spherical mirror with radius of 50 cm has a 10 cm tall object placed 125 cm in front of it. What is the height of the image? (use both rays and equations
f=25 cm
What if it was convex?
" I would like a clearer explanation of paraxial rays. "
"Can I assume light will reflect off a straight mirror at 90 degrees and light will reflect off a bent mirror/lens will be perpendicular to that surface?"
Main Principles
Reflection
Mirrors
f is focal length in meters {m}
theta is angle measured from the normal to the surface
r is radius of spherical mirror {m}
do is distance to object {m}
di is distance to image {m}
m is magnification {m}
hi is height of image {m}
ho is height of object {m}
When we 'see' something, what is happening?
Thus there are two things we 'see'
Sources, and reflections.
We have talked about the source of light in the last few chapters
recall
Light is electromagnetic waves
Accelerating charges produce EM waves/Light
We say that light moves in rays, this means we say that a narrow beam of light will stay narrow.

This study is called Geometric optics.
It assumes that light moves in parallel bundles and that it doesn't bend.
This is a bit of a simplification but it is good enough
The Ray model of light.
The law of reflection says that the angle of incidence is equal to the angle of reflection.
And it lies in the same plane as well.
NOTE: we measure all angles off of the Normal.
So why doesn't this always work?
The law of reflection says that incoming angle
equals outgoing angle.

Diffuse reflection

Not all surfaces are flat. Look at this picture.
Diffuse reflection still obeys the law of reflection but the surface simply isn't flat.
Plane mirrors
Glass can be made very flat, then a highly reflective material is placed on the back.

In the mirror however you will see yourself, looking like you are standing on the other side of the mirror, facing you.
What you see is an image (amazing I know)
For plane mirrors this distance from the object to the mirror is the same distance from the image to the mirror
Note that the rays don't actually go through the mirror and come from the apparent source
Thus it is called a virtual image
Virtual images won't be seen on a piece of paper held at the observed spot.
An image vs an object.

An object is the source of the light ray
It technically doesn't have to be a tangible object
but most often it is
so when you stand in front of a mirror you are the object.
Does a 'full length' mirror need to be as tall as a person?
A. Yes
B. No
Spherical mirrors
Two types of mirrors that are formed as part of a sphere.
Concave
Convex
If you follow the principal axis (line perpendicular to the mirror from its center.
The distance from the mirror to the focal point is the focal length.
Here 'O' is the center of the circle, note the relationship of radius to the focal length

f = r/2
This picture also introduces ray diagrams
Light rays come in everywhere, but they also do very specific things, and with a curved mirror they will form an image depending on the focal length and how far the object is away from the mirror.
so back to concave mirrors
Concave mirrors reflect light back to the center
If the mirror is 'small' compared to the radius of the mirror itself, then we can say the light will all reflect to the same point
Focal point
Three rays to trace each has two steps
1. Parallel then back through F
2. Through F then back parallel
3. Through C and to the mirror
Note goes both ways
Now this is very nice, and you can estimate distances
but
there is a way to calculate this as well.
You'll also note the size of the image is different than the object. This leads to the concept of magnification.
If my object distance is greater than the focal length what type of image will be formed
A. Virtual upright
B. Virtual inverted
C. Real upright
D. Real inverted
Now there was one more option for concave lenses
what if the object is inside the focal length?
This one makes a larger virtual image, note the light rays don't actually go to the image, but appear to.
Convex mirror
Convex mirrors will always form virtual images,
that are smaller.
Note, the focal point is behind the mirror.
Important note before we move on to problems.

The equations to solve these are heavily dependent on signs.

so we need a table.
Technically you could just say
+ if on reflective side
- if behind mirror

(this works for f, do and di.
• Can I assume light will reflect off a straight mirror at 90 degrees and light will reflect off a bent mirror/lens will be perpendicular to that surface?
• I would like a clearer explanation of paraxial rays.
• When you look in a mirror do you see things with as much detail as you would seeing them the same distance you are from the mirror, or twice that distance?
• How come our eyes assume that the image we see in a mirror is right in front of us and not behind us? Does it have to do with the ray model? How come concave mirrors magnify and convex mirrors widen the view? Does it have to do with how these types of mirrors bend light? Do perfectly parallel lines follow the law of reflection since they don't come to the mirror at an angle?
• How can the angle of incidence equal the angle of reflection?
• i need help understanding how to properly set up a problem using the spherical mirror and the reflection problems. i'm having trouble understanding when to substitute variables into other equations.
• Why can our eye only absorb small bundles of light and how does that allow us to see so many things at one time, and how does that relate to our peripheral vision? Is how much light that is absorbed or reflected only determined by the type of material it hits? Can we talk about how whether the mirror is flat, convex, concave changes the light reflected and what we see?
• In section 23-3 there is a subsection on Image Formation and Ray diagrams, my question is where do we see the application of this principle, I understand that this will play a role into things as rays pass through concave pieces of glass but is there any other application with this?
• I did not understand the section talking about concave mirrors. I understood the images but not application/math. Could we run through some mathematical examples?
• when we see an object and it has a color and a shape as we see it that must be light, but is it just a reflection of light? what are we seeing when we see an object?
• Is the ray being reflected off of a convex mirror tangent to the mirror?
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