Reflection and Refraction
Consider a ray of light that strikes a plane mirror at some angle θi , as shown below. This angle is
called the angle of incidence and is measured from the normal - a line perpendicular to the mirror
where the ray strikes.
Normal
θi
θr
Mirror
The ray will be reflected back from the mirror at some angle θr ; this angle is called the angle of
reflection and is again measured relative to the normal.
The law of reflection states that
θi = θr
(1)
Now consider a ray of light in air that strikes a transparent object such as glass with angle of incidence
θ1 .
Normal
θ1
n1
n2
θ2
Here, the ray will be refracted into the glass with angle θ2 . Snell’s law states that
n1 sin θ1 = n2 sin θ2
The quantity n is called the index of refraction and is a physical property of each medium; roughly, a
measure of its optical density.
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In the situation shown above, n1 = 1 for air/vacuum so
n2 =
sin θ1
sin θ2
(2)
and can be used to determine the index of refraction n2 of the glass.
Apparatus
Cork board, Free-standing mirror, Glass rectangular solid, Paper, Straight pins, Rule, Protractor.
Procedure
1. The procedural setup for reflection is shown below.
Mirror
45◦
Pin
Pin
Normal
View
2. Take a sheet of paper and draw a line across the middle, long side to long side; this will represent
the location of the mirror. On one side of this line, draw a perpendicular line from the mirror
line to the edge of the paper; this will be the normal. On one side of the normal, draw a line 45◦
from the normal extending from the mirror to the edge of the paper. Label this line with some
arrows pointing back toward the mirror; this line will represent an incoming ray of light.
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3. Place the paper on the corkboard and then the mirror on the paper with the silvered surface of
the mirror on the line you drew previously. Place two pins on your incoming light ray; they need
to be at least 5cm from the mirror and at least 5cm from each other.
4. Now, look from table level on the other side of the normal toward the mirror; this vantage point
is indicated in the figure above.
5. Move your head from side to side until the image of the two pins line up; i.e., appear as one
pin. Place a pin on this side of the normal at a location where all three line up; again, at least
5cm/5cm. Repeat with a second pin.
6. Remove all the pins and mirror and place your paper on the table. Draw a line from where the
incoming ray hits the mirror (the normal) through your two pin points. Label this line with some
arrows pointing away from the mirror; this line will represent the reflected ray of light. Measure
the angle this line makes with the normal.
7. Repeat the procedure with incoming rays of 30◦ and 60◦ from the normal; use the same sheet of
paper.
8. The procedural setup for refraction is shown below.
Pin
Normal
Pin
45◦
Block
View
9. Take a clean sheet of paper and rotate it to landscape orientation. Place the glass block in the
center of the paper and draw its outline on the paper. Draw a normal on one side extending
from the edge of the paper through the entire block (remember the refracted ray is in the block).
Draw an incoming ray 45◦ from the normal.
10. Place the paper on the corkboard and position the block in its outline. Place two pins on the
incoming ray; here, at least 3cm from the block and 5cm apart.
11. Now, look from table level from the other side of the block back through the block; this vantage
point is indicated in the figure above.
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12. Move your head from side to side until the image of the two pins in the block line up. Place a pin
on this side of the block at a location where all three line up; again, at least 3cm/5cm. Repeat
with a second pin.
13. Remove all the pins and block and place your paper on the table. From the other side of the
block from your incoming ray draw a line that goes through both pin points extending from the
black to the edge of the paper. Label this line with some arrows pointing away from the block;
this line will represent the refracted ray of light once it leaves the block. Draw a line from where
your incoming ray hits the block to where the refracted ray leaves the other side of the block (it
had to travel in a straight line through the block).
14. We are interested in the refraction that happened at the top surface of the block; i.e., where the
incoming ray strikes the block. Measure the angle the line through the block makes with the
normal. Calculate the index of refraction of the block.
15. Repeat the procedure with incoming rays of 35◦ and 55◦ from the normal; use the same sheet of
paper. Calculate the average index of refraction.
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Data Sheet
Trial
θi (◦ )
1
45◦
2
30◦
3
60◦
Trial
θ1 (◦ )
1
45◦
2
35◦
3
55◦
θr (◦ )
θ2 (◦ )
n
Average n
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Analysis
1. Did you verify the Law of Reflection? Why or why not?
2. Suppose you did the procedure in reverse; i.e., directed the incident ray along the original path
of reflection. Would the reflected ray follow the original path of incidence? Why or why not?
3. What is the percent error in the index of refraction? Do you feel that the concepts and equations
here were verified? Why or why not?
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4. If the light ray originated within a medium more dense than air, then moved to air through the
surface (such as at the bottom edge of the block here), would the refracted ray be bent toward
or away from the normal at this surface? Why?
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