To measure index of refraction of a glass cube and a plastic prism.
A glass cube, 4 pins, a plastic prism, incline plane, laser
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 qi /sin qr.
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 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.
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.
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.
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, qt
, 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 qt,
and a careful geometric derivation of the relationship between qt
and qc will allow you to calculate
the index of refraction of the prism's material from Snell's equation:
n=1/sin qc, 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.
Graph sin qi as a function of sin qr. 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?
Perform geometric derivation of the relationship between qt
and qc . Use your measured qt
find qc 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?