The angle between the two refracting surfaces of a total reflecting prism is

Options

A. `90^@`
B. `60^@`
C. `45^@`
D. `30^@`

Answer

To solve the question regarding the angle between the two refracting surfaces of a total reflecting prism, we can follow these steps:

### Step-by-Step Solution

1. **Understanding the Total Reflecting Prism**:
A total reflecting prism typically has two reflecting surfaces. For example, consider a prism with angles of 45 degrees at each of the two refracting surfaces.

2. **Identifying the Angles**:
In a common total reflecting prism, the angle between the two refracting surfaces is crucial for understanding how light behaves when it enters and exits the prism.

3. **Analyzing the Geometry**:
In a right-angled prism where both refracting surfaces are at 45 degrees, the angle at the apex of the prism (the angle between the two refracting surfaces) can be calculated.

4. **Calculating the Angle**:
The total angle in a triangle is 180 degrees. In our case, if each of the two angles is 45 degrees, the angle between the two surfaces can be calculated as:
\[ 90^\circ = 180^\circ - (45^\circ + 45^\circ) \]
This shows that the angle between the two refracting surfaces is 90 degrees.

5. **Conclusion**:
Therefore, the angle between the two refracting surfaces of a total reflecting prism is 90 degrees.

### Final Answer
The angle between the two refracting surfaces of a total reflecting prism is **90 degrees**.

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