If a light ray incidents normally on one of the faces of the prism of refractive index 2 and the emergent ray just grazes the second face of the prism, then the angle of deviation is

Options

A. `0^(@)`
B. `30^(@)`
C. `45^(@)`
D. `60^(@)`

Answer

To solve the problem, we need to determine the angle of deviation when a light ray strikes a prism normally and the emergent ray just grazes the second face of the prism.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- A light ray is incident normally on one face of a prism with a refractive index \( \mu = 2 \).
- The emergent ray just grazes the second face of the prism.

2. **Identifying the Critical Angle**:
- When the emergent ray grazes the second face, it means that the angle of refraction at that face is \( 90^\circ \).
- The critical angle \( C \) can be calculated using Snell's Law:
\[ \mu \sin C = \sin 90^\circ \]
- Since \( \sin 90^\circ = 1 \), we have:
\[ 2 \sin C = 1 \]
- Therefore,
\[ \sin C = \frac{1}{2} \]
- This gives us:
\[ C = 30^\circ \]

3. **Calculating the Angle of Deviation**:
- The angle of deviation \( \delta \) is given by the formula:
\[ \delta = 90^\circ - C \]
- Substituting the value of \( C \):
\[ \delta = 90^\circ - 30^\circ = 60^\circ \]

4. **Conclusion**:
- The angle of deviation \( \delta \) is \( 60^\circ \).

### Final Answer:
The angle of deviation is \( 60^\circ \).

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