LivePhoto Physics Activity 33
Name: ___________________________
Date: ____________________________
Snell’s Law of Refraction
Have you ever wondered what causes mirages, how lenses can focus light, or why your feet look closer
and bigger in a pool of water than you know they are? All these phenomena can be explained using the
concept of refraction and an experimentally validated equation known as Snell's Law.
When light travels through a vacuum or a dilute gas such as air, it does so at the incredible speed of
cvac=3.00x108 m/s. Light travels more slowly in uniform transparent substances such as clear plastic and
water. If the speeds of light c1 and c2 are known in two isotropic substances1, Snell's Law can be used to
predict how the a light beam will refract or change its direction when traveling from one substance to
another. It can be expressed as
1
1
sin θ1 = sin θ 2 [Snell’s Law] (Eq. 1)
c2
c1
Here θ represents the angle between the direction of the
light beam and a normal line (defined as the line
perpendicular to the two surfaces at the point where the
light ray passes from one substance to another, as shown
in Figure 1.)
Another way of expressing Snell’s Law is in terms of the
index of refraction of each substance, labeled n1, n2 etc. It
is defined as the factor by which light is "slowed down"
within a dense transparent substance such as Acrylite®,
glass, or water compared to its velocity in a vacuum. By
definition
c
n1 ≡ vac [index of refraction definition] (Eq. 2)
c1
and Snell’s Law can be rewritten as
Normal
θair
Air
®
Acrylite
θac
Light
Source
Figure 1: A bird’s eye view of a beam of light
traveling through a transparent acrylite block and
then bending as passes into air.
n1 sin θ1 = n 2 sin θ 2 (Eq. 3)
Your tasks in this activity are twofold (1) to provide experimental verification of Snell’s Law; and (2) to
use the Law to determine the speed of light in Acrylite, which is a clear plastic often used to make lenses.
You can complete this activity by using the Logger Pro software to analyze a video clip entitled <Acrylite
into air.mov>. This clip shows a beam of light passing through a thick semi-circular shaped block of
Acrylite plastic into air. The beam is rotated though a series of different angles with respect to a normal
line that is perpendicular to the boundary between the two substances. For example, Figure 1 shows a
video frame for which the angle of the incidence with respect to the normal of θ ac = 37o while the
refracted beam has an angle with respect to the normal of θ air = 64 o .
Before proceeding with this activity we suggest that you use QuickTime Player to view the movie
entitled <Acrylite into air.mov> and browse through it one frame at a time. Note: Using the arrow keys on
the computer keyboard is probably the best way to view the movie one frame at a time.
1
An isotropic substance allows light to travel through it at same speed in any direction. Snell's law is generally true only for
isotropic substances (such as glass). In crystals that are not isotropic, birefringence may split the refracted ray into two rays
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1. Preliminary Questions
Note: You will receive full credit for each prediction made in this preliminary section whether or not it
matches conclusions you reach in the next section. As part of the learning process it is important to
compare your predictions with your results. Do not change your predictions!
(a) Use the fact that the speed of light in air is 99.97% of that in a vacuum so that c air ≈ c vac , what is the
value of the index of refraction for air? Explain your reasoning or show your calculations and round
your answer to four significant figures.
nair
≈
(b) When the light beam passes from Acrylite to air does it bend toward the normal line or away from
the normal line? Explain
(c) Based on your answer to part 1(b) above do you expect the index of refraction for Acrylite, nac, to be
greater than, less then or the same as the index of refraction for air, nair? Explain your reasoning
(d) If Snell’s Law holds and you plot a graph of sin(θ air ) vs. sin(θ ac ) what should the shape of that graph
be? What would the slope (or slopes of that graph) represent? Explain,
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Physics with Video Analysis
2. Activity-Based Questions
Verify Snell’s law and determine the index of refraction for Acrylite: To complete these tasks you’ll
need to obtain data from the movie for the angle between the light beam and the normal before and after
it bends for several angles of incidence. Then you can use Logger Pro to: (1) calculate the sines of these
angles and (2) analyze a graph of sin(θair) vs. sin(θac).
(a) Collect basic data: Use the video clip <Acrylite into air.mov> to obtain the data below for several
angles of incidence and refraction and then transform these angles from degrees to radians using
three significant figure. Summarize your data and calculations in the table shown below. Note: You
can use the answers provided in Row 5 to verify your procedures for determining the requested
values.
θac(deg)
θair(deg)
θac(rad)
θair(rad)
75.0
0.70
1.31
0.0
10.0
20.0
31.5
40.0
(b) Use Logger Pro Software to verify Snell’s Law: In answering question 1(d) you should have noted
that if Snell’s Law holds the shape of a graph sin(θair) vs. sin(θac) should be a straight line and its
slope should give the value of the index of refraction of Acrylite denoted as nac.
(1) open the Logger Pro experiment file <SnellsLaw.cmbl> and fill in the values of θac(rad) and
θair(rad)
(2) direct Logger Pro to do the calculations needed to verify Snell’s Law by using the Calculated
Column feature in the Logger Pro data menu to create a graph of sin(θair) vs. sin(θac);
• Double-click the column header for sin(θac) to view the Calculated Column Options dialog box.
Enter the equation to calculate the dimensionless value for the Sine of θac(rad) values that you
entered into the Logger Pro column.
• Next repeat the process by double-clicking on the column header for sin(θair). Enter the equation
to calculate the dimensionless values for the Sine of θair(rad); and
(3) then summarize the procedures you used and your results. Also sketch the graph of sin(θair) vs.
sin(θac) data in the graph frame shown below.
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(c) Determine the index of refraction for Acrylite: List the dimensionless index of refraction below
and explain how you determined it.
nac = ___________
(d) Speed of Light in Acrylite: What is the speed of light in the block in meters/second? How did you
determine it? Report your answer to 3 significant figures.
cac = ___________
(e) THE CRITICAL ANGLE: The later frames in the movie show that once the angle of incidence, θac ,
leads to an angle of refraction , θair , that is greater than 90° the light beam does not emerge from the
Acrylite. This angle of incidence for which refraction becomes impossible is called the critical angle.
Use Snell’s Law along with your calculated value of the index of refraction for the Acrylite and the
value of θair=90° to calculate the expected value for the critical angle at the Acrylite-air interface.
Check your answer by looking at the movie and reading the critical value of θac using the protractor
in the video clip.
θ critical = ___________
3. Reflections on Your Findings
(a) If the index of refraction in water is about nwater = 1.33 which substance when shaped into a lens
would have the most focusing power, Acrylite, or water? Explain.
(b) How might the critical angle phenomenon be used to allow light travel in a curved path in an optical
fiber that is not straight? Explain.
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Physics with Video Analysis