Index_of_Refraction

Introduction. When a ray of light passes obliquely from air into glass, the ray abruptly changes its direction at the boundary between the two media. A ray traveling toward a boundary between two media of different optical densities is an incident ray; the same ray moving away from the boundary in the new medium is the refracted ray. The normal is the line drawn perpendicular to the boundary surface at which the light ray enters the new medium. The angle of incidence qi is measured between the incident ray and the normal and the angle of refraction qr is measured between the refracted ray and the normal.

When a ray passes from air into a medium of greater optical density such as glass, the ray bends toward the normal and forms the refracted ray. When a ray leaves a denser medium to re-enter a less dense medium, the ray bends away from the normal. Refraction occurs when the speed of light changes from one medium to another.

The index of refraction n of any transparent material is defined as

n = (Speed of light in a vacuum)/(Speed of light in the medium)

Since the speed of light in a vacuum is greater than it is in any other medium, the ratio of speeds must always yield a number greater than 1 for transparent media. Furthermore, this number is dimensionless, that is, it does not carry a unit because it is a ratio of two measurements with identical units that cancel. Thus, the index of refraction of water is very nearly 1.33 and the index of refraction of different kinds of glass ranges from 1.5 to 1.8.

The speed of light in air is almost equal to the speed of light in vacuum so that it is permissible to use the speed of light in air for this experiment. Thus:

n = (Speed of light in air)/(Speed of light in the material)

Since a direct measurement of the speed of light in the student laboratory is beyond our ability, we use an indirect method which involves Snell's Law. In its most general form for an air-glass combination, Snell's Law is written as

nasinqa = ngsinqg

In this relationship, na is the index of refraction in air, ng is the index of refraction in glass, qa is the angle between the ray and the normal (to the air-glass boundary) in air, and qg is the angle between the ray and the normal (to the air-glass boundary) in glass. However, if we take the speed of light in air to be equal to the speed in vacuum, then na = 1 and Snell's Law becomes

sinqa = ngsinqg or ng = sinqa/sinqg

Regardless of the direction of a ray with respect to the boundary between the two media, the angle in air is consistently written in the numerator and the angle in the medium is consistently written in the denominator. Thus we can write Snell's Law in specific form as

ng = (Sine of the angle in air [or vacuum])/(Sine of the angle in the glass)

Strategy. The laboratory equipment will be arranged so that the paths of a number of rays of light can be observed as they pass from air to glass. You will measure the angle of incidence qi and the angle of refraction qr for each of these rays and then you will construct a graph showing the relationship between the sines of the various angles of incidence and the sines of the corresponding angles of refraction. The index of refraction for the glass block will be deduced from this graph and compared with the mean index of refraction for the same block obtained by directly applying Snell's Law.

Getting Started. The technique for tracing a ray of light from air into glass should be mastered before you begin your actual measurements. On a sheet of practice paper, outline the rectangular glass block and then draw a straight line to the one edge of the outline at an angle of approximately 40 or 50 degrees. Label the intersection B and the line you have drawn as AB. Line AB now represents the path of an incident ray of light going from air to glass. Place two straight pins vertically at locations A and B.

Replace the block exactly on its outline. On the opposite side of the block, sight along one edge of a ruler through the block to ray AB. Sighting along the ruler is very much like aiming a rifle. In this instance, aligning the images of the straight pins, that is, seeing only one image, will give you the direction of the ray.

Move the ruler about until the image of the aligned straight pins and the edge of the ruler appear to form a straight line. Then draw a pencil line along the sighting edge of the ruler a short distance. Remove the block and extend the line you have just drawn to the block outline. The intersection of the line and the outline is labeled C and the line is CD. Now join point B to point C with a straight ruled line. The line represents the ray of light within the glass so that the line ABCD indicates the path of the ray going from air, into and through the glass, and emerging into the air once more toward the eye of the observer. BC is the fist refracted ray. Practice this sighting procedure several times before proceeding with the experiment.

Materials

Rectangular glass block

Metric ruler

Protractor

11" x 17" (27.9 cm x 43.2 cm) unruled paper

Graph paper

2.5H pencil with eraser

12" x 18" (30.4 cm x 45.7 cm) sheet of styrofoam presentation board

Two small strips of masking tape

Two straight pins

Reference Tables for Physics

Calculator

Procedure

1. Place the sheet of unruled paper on the styrofoam presentation board and attach with two small strips of masking tape.

2. Draw two outlines of the block on the sheet of paper. Remove the block; then construct normals NN' for each outline extending through the upper air-glass surface near the left side of the outline. Label this point B. Insert a straight pin into the paper vertically at this point.

3. Using either of the two outlines draw the line AB at an angle of 20 degrees to the normal of approximately 10 cm in length. Label the end A. Insert a straight pin into the paper vertically at this point. Label this line "incident ray". Proceed as before, replacing the glass block exactly within its outline, sighting along the edge of the ruler through the glass to ray AB. (Note that the vertically placed pins will form a single image when perfect alignment with ray AB is achieved.) Then draw in this line right to the air-glass boundary. This intersection is labeled C. Draw in a line from point C in line with ray AB that is approximately 10 cm in length. Label the end D.

4. Remove the glass block. Then draw in line BC with the ruler and label this line "refracted ray". Each line segment (AB, BC, CD) should carry a directional arrow.

5. Label angles qi (angle of incidence) and qr (angle of refraction). With a protractor, measure the angle of refraction (qr) in the glass and record in the table of values. Next, look up the sines of both angles qi and qr in your calculator and enter these values into the data table to three significant figures.

6. Repeat the above procedure for angles of incidence of 0 degrees, 40 degrees and 60 degrees, using a different outline of the block for each new angle of incidence.

Data Table

qi (air)

qr (glass)

Sinqi

Sinqr

n = Sinqi/Sinqr

0 degrees

_____

________

____

20 degrees _____

________

____

_____________

40 degrees _____

________

____

_____________

60 degrees _____

________

____

_____________

Mean

_____________

Data Analysis

1. Compute and record in the Data Table the indices of refraction for each of the angles except 0 degrees. The determine the mean value of n and record.

2. Plot the four values of Sinqr so that you can draw a graph versus Sinqi along the y-axis and Sinqr along the x-axis. If your measurements are carefully made, the graph will be a straight line going through the origin. The straight line should be drawn as a "best-fit" for your points.

3. Determine the slope of the straight line graph (slope = Sinqi/Sinqr). Then calculate the percent error between the mean value of n as shown in the Data Table and the slope as calculated.

4. Obtain the "accepted" or manufacturer's value of the index of refraction from your instructor and calculate the percent error between your mean value of n and the accepted value.

Questions

1. a. Does the ratio Sinqi/Sinqr yield a consistent value for the angles of incidence you

used?

b. What special name is assigned to this particular ratio?

2. a. As the angle of incidence is increased, what change is observed in the angle

of refraction?

b. Is the ratio Sinqi/Sinqr dependent on or independent of the magnitude of the angle

of incidence?

3. Referring to your Data Table, why were you told to omit the calculation of n for the

angle of incidence equal to 0? Explain.

4. Identify your glass block as flint glass, crown glass, and so on by consulting your

Reference Tables for Physics.

5. Calculate the speed of light, in meters per second, in the glass block you used in this

experiment. (Hint: The first equation given in this experiment may be used to

obtain this answer.)

6. To six significant figures, the speed of light in vacuum is 2.99793 x 10exp8 m/s. If the

index of refraction of dry air is 1.00029, calculate the speed of light in dry air.