In this experiment, you will investigate the deviation of light through a hollow triangular prism filled with water and use the angle of minimum deviation t...
Question 1 Report
In this experiment, you will investigate the deviation of light through a hollow triangular prism filled with water and use the angle of minimum deviation to calculate the refractive index of water. The hollow prism is made from three flat glass plates sealed together to form a triangular cross-section with a prism angle A = 60°.
Fig. 7.1 shows the arrangement. The hollow prism is placed on white paper and filled carefully with water. A narrow ray of light from a ray box is directed at one face of the prism at an angle of incidence i to the normal. The ray refracts as it enters the water, travels through the water, and refracts again as it emerges from the second face. The angle of deviation D is the angle between the original direction of the incident ray (extended forward as a dashed line) and the direction of the emergent ray.
Mark the incident ray and the emergent ray with pins for each angle of incidence. Remove the prism and draw both rays. Extend the incident ray forward and measure the angle D between this line and the emergent ray using a protractor. Repeat for angles of incidence i = 30°, 35°, 40°, 45°, 50°, 55° and 60°. The results are shown in Table 7.1.
| Angle of incidence i / ° | 30 | 35 | 40 | 45 | 50 | 55 | 60 |
|---|---|---|---|---|---|---|---|
| Angle of deviation D / ° | 25 | 24 | 24 | 23 | 24 | 25 | 26 |
(a) Record the angle of deviation D when i = 45°. [1]
(b) State the angle of incidence at which the deviation is smallest. Record this minimum deviation Dmin. [1]
(c) Use the formula n = sin((A + Dmin) / 2) / sin(A / 2) to calculate the refractive index of water. Show your working. [3]
(d) Describe how D changes as i increases from 30° to 60°. [1]
(e) Explain why a glass prism with the same angle A gives a larger minimum deviation than this water prism. [1]
(f) State one precaution the student should take when filling the hollow prism. [1]
(g) Measure the angle of deviation D from the ray diagram in Fig. 7.1. Record your value. [1]
(h) State one advantage of using the minimum deviation method to find the refractive index rather than measuring refraction at a single surface. [1]
Answer Details
(a) From Table 7.1, when \( i = 45° \), the angle of deviation is D = 23°. [1]
(b) The minimum deviation occurs at i = 45°, giving Dmin = 23°. [1]
Examining the data: D decreases from 25° at i = 30° to 23° at i = 45°, then increases again to 26° at i = 60°. The smallest value is 23°.
(c) Using the minimum deviation formula: [3]
\[ n = \frac{\sin\!\left(\frac{A + D_{\min}}{2}\right)}{\sin\!\left(\frac{A}{2}\right)} \]
Substituting \( A = 60° \) and \( D_{\min} = 23° \):
\[ n = \frac{\sin\!\left(\frac{60 + 23}{2}\right)}{\sin\!\left(\frac{60}{2}\right)} = \frac{\sin(41.5°)}{\sin(30°)} \] [1]
\[ n = \frac{0.663}{0.500} \] [1]
\[ n = 1.33 \] [1]
This matches the accepted refractive index of water.
(d) As \( i \) increases from 30° to 60°, D first decreases from 25°, reaching a minimum of 23° at around \( i = 45° \), and then increases again to 26° at \( i = 60° \). The pattern is U-shaped. [1]
(e) Glass has a higher refractive index than water (typically \( n \approx 1.5 \) vs 1.33). A higher refractive index means light is bent more strongly at each surface, producing a greater total deviation for the same prism angle. [1]
(f) Fill the prism slowly to avoid trapping air bubbles inside. Also check for leaks at the seams and ensure the water level reaches the top of the prism so the water surface does not interfere with the ray path. [1]
(g) Measured value from the ray diagram in Fig. 7.1: approximately 25° (accept values in the range 23-30°). [1]
(h) At minimum deviation, the ray passes symmetrically through the prism and the result is least sensitive to small errors in measuring the angle of incidence. This gives a more reliable and reproducible value of \( n \) than measuring refraction at a single surface. [1]
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