A prism can have a maximum refracting angle of `(theta_C=`critical angle for the material of prism )

Options

A. `60^@`
B. `theta_C`
C. `2 theta_C`
D. slightly less than `180^@`

Explanation

To solve the problem regarding the maximum refracting angle of a prism in relation to the critical angle, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Critical Angle:**
The critical angle (θ_C) is the angle of incidence above which total internal reflection occurs when light travels from a denser medium to a less dense medium. For a prism, this is the angle at which light will not emerge from the opposite surface.

2. **Identify the Condition for No Emergence:**
If light is incident on the opposite surface of the prism at the critical angle (θ_C), it will not emerge from that surface. This means that the angle of incidence at the second surface equals the critical angle.

3. **Relate the Angle of Prism to Critical Angle:**
For a prism with a refracting angle A, when light is incident at the critical angle on the opposite surface, the angle of incidence at that surface is equal to θ_C.

4. **Derive the Maximum Refracting Angle:**
The condition for no emergence from the second surface implies that the angle of the prism (A) must be greater than twice the critical angle. This is because the light must bend sufficiently within the prism to reach the critical angle at the second surface.

Therefore, we can express this relationship as:
\[ A_{max} = 2 \theta_C \]

5. **Conclusion:**
The maximum refracting angle of the prism, under the condition of no emergence from the opposite surface, is:
\[ A_{max} = 2 \theta_C \]

### Final Answer:
The maximum refracting angle of the prism is \( A_{max} = 2 \theta_C \).

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