Reflection, Refraction and Polarization
Reflection and Refraction
Pre-lab questions and Exercises
Which one quantity is being measured by at least two different methods in this experiment?
How will you determine which method is most precise and which is most accurate?
The lab does not take into account the dispersion of light through a medium (this means that the
index of refraction depends on the frequency of light). How might this affect your results?
Are there lower or upper bounds on the index of refraction for a material?
What is a practical application or use for the total internal reflection?
Introduction
The Law of Reflection
When a ray of light strikes a plane mirror, the light
ray reflects off the mirror and changes its direction
of travel. By convention, the direction of a light
ray is expressed as the angle the light ray makes
with the line normal to the surface. The angle of
incidence is the angle between the normal and the
incident ray. The Law of Reflection states that the
angle of incidence equals the angle of reflection.
𝜽𝒊 = 𝜽𝒓
Refraction
When a ray of light strikes the surface of a
piece of transparent material, the beam is split —
part of the beam is reflected from the surface,
while the rest is transmitted into the material.
The most common example of refraction is the
bending of light when it travels from water to air,
which causes submerged objects to appear
displaced from their actual positions. Experiment
has shown (and you will verify in this lab) that
the angle of the reflected light is equal to the
angle of the incident light (both angles are
conventionally measured with respect to a line
normal to the surface). For the transmitted ray,
the path the light takes is bent as it passes from
one medium into another. This bending of the
light ray is known as refraction. The angle of the
Figure 1
refracted ray is related to the angle of the incident
n1 sin1  n2 sin 2
ray (see Fig. 1) by Snell’s Law, also known as the Law of Refraction:
(1)
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Reflection, Refraction and Polarization
where n1 and n2 are the indices of refraction of medium 1 and medium 2, respectively. The index of
refraction of a material is defined to be the ratio of the speed of light in vacuum to the speed of light
in the material, n = c/v. The index of refraction of air varies only slightly (<0.03%) from one, and for
this experiment is taken to be one, i.e. nair = 1.
Total Internal Reflection
If light passes from one medium into another
medium of smaller n, the angle of refraction will
be larger than the angle of incidence. At the
critical angle of incidence,  c , the angle of
refraction will reach 90°. The “transmitted” light
is not transmitted into the second medium, but
travels along the boundary of the two media,
parallel to the surface (see Fig.2). For incident
angles greater than the critical angle, all the light
is reflected back into the first medium; this
condition is known as total internal reflection.
Since the critical angle is the angle for which the
refraction angle is 90°, we have sin 1 = sin 90° =
1. Equation (1) gives:
Figure 2
sin  c  n1 n 2 .
(2)
Procedure
Part 1 – Reflections
Does the law of reflection apply to curved surfaces like it does to flat surfaces? How can you use
the triangular reflective optics piece to answer this question? Give an explanation for the results you
observed.
Part 2. Snell’s Law and Index of Refraction
In this part of the experiment you will study the reflection and refraction of light from a plane
separating two media (air and acrylic). You will verify that the path of the refracted light satisfies
Snell's law, and as a result, you will determine the index of refraction of acrylic.
Place the semi-circular piece of acrylic in the middle of a sheet of paper. Use a pencil to trace around
the perimeter of the component.
Use the light source to shine a single ray of light toward the center of the flat side at a 45⁰ incident
angle.
Trace the rays going in and coming out of the acrylic.
Remove the acrylic piece and connect the two rays to show the path that light followed while inside
the acrylic.
Use the protractor to measure the angle of refraction that the light ray makes with the normal line at
the interface and record your values.
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Reflection, Refraction and Polarization
Repeat the process for an initial incident angle larger than 45° and then for an initial incident angle
smaller than 45°.
Part 3. Internal Reflection
In this part of the experiment, you will observe that light cannot pass from a medium (acrylic
disk) into another medium (air) with a lower index of refraction if the angle of incidence is greater
than the critical angle, given by Eq. (2). The light is totally reflected back into the medium. You will
measure the critical angle of the acrylic and use Eq. (2) to determine its index of refraction.
Send light from the light source towards the circular face of the component. In this way the ray will
approach the flat side of the disk from the acrylic side and exit on the side with air (lower index of
refraction). (Why is this geometrical arrangement important?)
Starting from a small angle of incidence (near 0°), gradually increase the incident angle by rotating
the light source.
As the incident angle approaches the critical angle, the refracted ray will approach the flat side of the
disk. Determine the angle when the refracted ray just disappears and record the angle as 𝜃𝑐 .
Estimate the uncertainty in your measurement of  c .
Data Analysis
The two parts of the lab allowed you to measure n, the index of refraction for acrylic. Determine n
and its associated uncertainty for each section of the lab.
Discussion (answer these questions directly on your worksheets)
Summarize the index of refraction derived from Parts 2, and 3. Compare your results with the
value of 1.49 for the index of refraction for acrylic. Which of your measurements is most precise?
Which is most accurate? What is your average value for n?
In performing Part 2, what difficulties did you encounter in measuring the angle of refraction at
large angles of incidence? How would you take this problem into account in the analysis of your
data? Are your results consistent with Snell's Law? Explain. If not, to what do you attribute the
differences?
In Part 3, describe the changes in the intensities of the reflected and refracted rays as the angle of
incidence approached the critical angle.
What is the speed of light in your acrylic?
What did you learn from this lab that may benefit you in the future?
What is the largest source of error in the experiment?
How would you improve the experiment in the future?
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