Experiment ( )

Measurement of the refractive index of a small quantity of liquid using the critical angle method

Object: To measure the refractive index of a small quantity of liquid.

Apparatus: rectangular glass block, drawing board, adhesive tape, drawing pins, protractor, liquid (water).

Background knowledge:

The experiment consists of two parts: A and B.

We use drawing pins to trace the path of a light ray.

In part A of the experiment, on 2 opposite sides of a rectangular glass block, we erect 2 drawing pins on a drawing board at positions where they appear to be in line, as shown in Figure 1. The line joining the positions of the pins shows the path along which a light ray would pass through the block. By measuring the angles of incidence and refraction, the refractive index hg of the glass block can be found.

In part B, we trace the critical ray passing through a thin film of liquid (water) and the glass block, as shown in Figure 2. The critical angle c in the glass block can be found. By using the values of hg and c, we can calculate the value of the refractive index h of the liquid.

Procedure:

Part A: Measuring the refractive index of glass (hg)

1.   Fix a sheet of paper on a drawing board. Place a glass block in the middle and draw accurately its outline ABCD.

2.   Place 2 drawing pins, P1 and P2, on one side of the block, as shown in Figure 1. Look through the other side and place 2 other pins, P3 and P4, so that they appear to be in line with P1 and P2.

3.   Mark the positions of the 4 pins. Remove the block and draw lines through them as in Figure 1.

4.   Measure the angle of incidence i and the angle of refraction r on both sides of the block. Calculate the value of the refractive index of glass hg.

5.   Repeat steps 2 to 4 and calculate the mean value of hg. Tabulate your results.

At boundary AD / At boundary BC
i/° / r/° / hg / i/° / r/° / hg

Mean value of hg = ______

Part B: Measuring the critical angle (c) and the refractive index of liquid (h)

6.   Fix another sheet of paper on the drawing board. Place the glass block in the middle and carefully draw its outline ABCD.

7.   Cut a small strip of paper of about 1 cm wide and of length equals to the thickness of the block. Draw a fine dark line down the middle of the strip. Smear it with the liquid (water) and stick it at X on the side AD so that the line is vertical.

8.   Look into the side CD with your eye near to C so that you can see the paper and the line clearly, as shown in Figure 2. Then move your eye towards D and notice that the line disappear suddenly from view at a certain point. Place 2 pins, P1 and P2, to mark the direction beyond which the line cannot be seen. Mark the position of the 2 pins and the position of the vertical line at X.

9.   Remove the glass block. Join P1 and P2 to meet CD at Y. Then join XY and measure the critical angle c for light passing from glass to water.

10.   Repeat steps 7 to 9 with different positions of the strip. Find the mean value of c.

Trial / Critical angle c/°
1
2
3
4
5
Mean of c =

11.   By applying Snell’s law for the refraction of light at the water-glass boundary at X, the refractive index of the liquid (h) can be found by:

h = hg sin c

Find the value of h.

Discussion:

1.   State any precautions that should be taken in order to improve the accuracy of the experiment.

2.   In step 11, the expression h = hg sin c can be used to find the value of h. Try to derive it from Snell’s law.

3.   From the separate values obtained for hg in part A, note the greatest divergence from the mean. Take it to be the maximum error in hg. State the value of hg along with its error accordingly.

4.   Find the maximum error in c in step 10.

where dc must be expressed in radian.

Hence calculate the maximum error in h and state its value accordingly.