A thin prism of `6^(@)` is made of material of refractive index `5/3`. The deviation caused by it is

Options

A. `2^(@)`
B. `8^(@)`
C. `4^(@)`
D. `6^(@)`

Answer

To find the deviation caused by a thin prism, we can use the formula for the minimum deviation (\( \delta_m \)) in terms of the prism angle (\( A \)) and the refractive index (\( n \)) of the material of the prism. The formula is given by:

\[ \delta_m = (n - 1) A \]

Where:
- \( \delta_m \) is the minimum deviation,
- \( n \) is the refractive index of the prism material,
- \( A \) is the prism angle.

### Step-by-Step Solution:

1. **Identify the given values:**
- Prism angle \( A = 6^\circ \)
- Refractive index \( n = \frac{5}{3} \)

2. **Substitute the values into the formula for minimum deviation:**
\[ \delta_m = (n - 1) A \]
\[ \delta_m = \left(\frac{5}{3} - 1\right) \times 6^\circ \]

3. **Calculate \( n - 1 \):**
\[ n - 1 = \frac{5}{3} - \frac{3}{3} = \frac{2}{3} \]

4. **Substitute \( n - 1 \) back into the equation:**
\[ \delta_m = \frac{2}{3} \times 6^\circ \]

5. **Perform the multiplication:**
\[ \delta_m = \frac{12}{3} = 4^\circ \]

6. **Conclusion:**
The deviation caused by the prism is \( 4^\circ \).

### Final Answer:
The deviation caused by the thin prism is \( 4^\circ \).

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