EXPERIMENT 1
INDEX OF REFRACTION LABORATORY
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OBJECT:
To measure index of refraction of a glass cube and a plastic prism.
APPARATUS:
A glass cube, 4 pins, a plastic prism, incline plane, laser
THEORY:
The index of refraction of a material is defined
experimentally to be the ratio of the sine of the
incident angle for light in a vacuum (or air) to the sine
of the refracted angle in that material, see Figure 1.
n= sin i /sin r.
The refraction (bending) of the beam occurs because
the light slows down in the material, so the index of
refraction is found to be the ratio of the speed of light
in a vacuum to the speed of light in a material,
n = c/v.
Figure 1. Path of a ray of light as it passes
from an optically less dense medium (like air)
into an optically more dense medium (like
glass).
The index of refraction is very useful, with some people claiming that all our knowledge of nature
can come from just knowing the index of refraction for different materials. General treatments of
this index have a complex mathematic relation, where n = no+ i nq, and i =  - 1. The index of
refraction is related to the electrical and magnetic properties of the atoms and molecules that make
up a material. This implies that we can relate microscopic properties (dielectric constants and
relative permeabilities) to macroscopic phenomena (the bending of light), which emphasizes the
importance of the measurement of the index of refraction.
PROCEDURE
Exercise 1.
A large glass (or plastic) cube is provided. Place the cube on a piece of cardboard that has been
covered with paper. Locate two pins on the far side of the cube. Sighting through cube, as shown
in Figure 2, locate two pins on the opposite side (closest to you) so that all the pins at aligned.
Carefully trace the outline of the cube faces onto the paper. Draw a straight line through each pair
of pins. Measure the angles of the incident and refracted beams, with respect to the line of the glass
cube, and NOT with respect to the normal! Determine angles of incidence and refraction with
respect to the normal by subtracting these measured angles from 90. Repeat these measurements
for at least five different angles.
Figure 2. The pins are the circles that are intersected by the dotted line. Your eye should sight
along the dotted line when positioning the pins.
Exercise 2.
A 60- 60- 60 prism is located on a board that rests on a table top as shown in figure 3. A laser
beam of light, traveling parallel to the table top, refracts upon entering the prism and may be
totally internally reflected as it tries to emerge from the opposite side of the prism. Whether or not
it is totally internally reflected depends upon the angle of incidence with that prism surface. If the
prism is lying on the table top, you will find for these prisms that the light does pass out of the
prism. However, if the prism is tilted, as shown in the figure below, there will be some minimum
angle, t , for which the laser light just starts to be totally internally reflected. For all angles greater
than this, the laser light is totally internally reflected. A careful measurement of the angle t, and a
careful geometric derivation of the relationship between t and c will allow you to calculate the
index of refraction of the prism's material from Snell's equation:
n=1/sin c, where n is the
index of refraction of the prism's material.
Figure 3. Schematic diagram of the Exercise 2 technique for determining the index of refraction.
DATA ANALYSIS
Exercise 1.
Graph sin i as a function of sin r. The straight line relationship between these data is obtained
for all combinations of (linear) optical media, not just air and glass, and is known as Snell's Law.
The slope of the straight line is the index of refraction. Using linear least squares analysis (or
appropriate data fitting program), calculate the index of refraction and the associated error in the
index from your data. Compare your results for n with known indexes of refraction (the tables are
available at the Lab or on the Internet. Indicate the source of information you used.) What material
is the cube?
Exercise 2.
Perform geometric derivation of the relationship between t and c . Use your measured t to find
c and n. Estimate the error for n. Compare your results for n with known indexes of refraction
(the tables are available at the Lab or on the Internet. Indicate the source of information you used.)
What material is the prism?