A thin glass prism of refractive index 1.5 produces a deviation of 4° of a ray incident at a small angle. What will be the deviation of the same incident ray by the same prism if it immersed in water of refractive index 4/3?

Question

Accepted Answer

To determine the deviation of a ray passing through a thin glass prism immersed in water, we need to consider the change in refractive index and how it affects the deviation angle.

1. **Explanation for Option 1 (Correct Answer):**

When a prism is in air, the deviation $ \delta $ is given by the formula:
   $$
   \delta = (n - 1)A
   $$
   where $ n $ is the refractive index of the prism and $ A $ is the angle of the prism. Given that the deviation in air is 4° and the refractive index of the prism is 1.5, we can express this as:
   $$
   4° = (1.5 - 1)A = 0.5A
   $$
   Solving for $ A $, we find:
   $$
   A = \frac{4°}{0.5} = 8°
   $$

When the prism is immersed in water, the effective refractive index $ n' $ of the prism with respect to water is given by:
   $$
   n' = \frac{n_{\text{prism}}}{n_{\text{water}}} = \frac{1.5}{\frac{4}{3}} = \frac{1.5 \times 3}{4} = \frac{4.5}{4} = 1.125
   $$

The deviation $ \delta' $ in water is then:
   $$
   \delta' = (n' - 1)A = (1.125 - 1) \times 8° = 0.125 \times 8° = 1°
   $$

Therefore, the deviation of the ray when the prism is immersed in water is 1°, which confirms that Option 1 is correct.

2. **Explanation for why other options are incorrect:**

- **Option 2 (2°):** This option assumes a larger deviation than calculated. The effective refractive index in water reduces the deviation, not increases it to 2°.
   
   - **Option 3 (8°):** This option suggests that the deviation remains the same as in air, which is incorrect because the refractive index of the surrounding medium (water) affects the deviation.
   
   - **Option 4 (16°):** This option implies a significant increase in deviation, which is not possible given the reduction in effective refractive index when the prism is immersed in water.

In conclusion, the correct deviation when the prism is immersed in water is 1°, making Option 1 the correct answer.