For the refraction of light through a prism

Options

A. For every angle of deviation there are two angles of incidence.
B. The light travelling inside an equilateral prism is necessarily parallel to the base when prism is set for minimum deviation.
C. There are two angles of incidence for maximum deviation.
D. Angle of minimum deviation will increase if refractive index of prism is increased keeping the outside medium unchanged if `mu_(p) gt mu_(s)`

Answer

To solve the question regarding the refraction of light through a prism, we will analyze the statements provided and determine their correctness based on the principles of geometrical optics.

### Step-by-Step Solution:

1. **Understanding the Angle of Deviation**:
- The angle of deviation (Δ) is defined as the angle between the direction of the incident ray and the direction of the emergent ray after passing through the prism.
- For a given prism, there is a specific angle of incidence (i) that results in the minimum angle of deviation (Δ_min).

**Hint**: Recall that the angle of deviation is minimized at a specific angle of incidence.

2. **Statement Analysis**:
- **Statement 1**: "For every angle of deviation, there are two angles of incidence."
- This statement is incorrect. The angle of deviation is a function of the angle of incidence, but for the minimum deviation, there is only one specific angle of incidence that corresponds to Δ_min.

**Hint**: Consider how the angle of deviation changes with varying angles of incidence.

3. **Light in Equilateral Prism**:
- **Statement 2**: "The light traveling inside an equilateral prism is naturally parallel to the base when a prism is set for minimum deviation."
- This statement is correct. At minimum deviation, the light ray entering and exiting the prism makes equal angles with the prism's base, thus becoming parallel to the base.

**Hint**: Visualize the path of light through the prism at minimum deviation.

4. **Maximum Deviation**:
- **Statement 3**: "There are two angles of incidence for maximum deviation."
- This statement is correct. For maximum deviation, there can be two different angles of incidence that yield the same maximum angle of deviation due to the symmetry of the prism.

**Hint**: Think about how the angles of incidence relate to the angles of refraction at the prism's surfaces.

5. **Effect of Refractive Index on Minimum Deviation**:
- **Statement 4**: "The angle of minimum deviation will increase if the refractive index of the prism is increased, keeping the outside medium unchanged."
- This statement is correct. As the refractive index (μ) increases, the minimum angle of deviation (Δ_min) also increases, as derived from the formula relating the refractive index to the angles.

**Hint**: Recall the formula relating refractive index, angle of prism, and angle of deviation.

### Conclusion:
- **Correct Statements**:
- Statement 2 (correct)
- Statement 3 (correct)
- Statement 4 (correct)
- **Incorrect Statement**:
- Statement 1 (incorrect)