A ray of light passing through a prism of refraction angle `60^(@)` has to deviate by atleast `30^(@)`. Then, refractive index of prism should be

Options

A. `lesqrt2`
B. `gesqrt2`
C. `gesqrt3`
D. `lesqrt3`

Explanation

To solve the problem of finding the refractive index of a prism given the angle of refraction and the angle of deviation, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Angle of the prism (A) = 60°
- Angle of deviation (D) = 30°

2. **Use the Formula for Refractive Index (n):**
The refractive index of the prism can be calculated using the formula:
\[ n = \frac{\sin\left(\frac{A + D}{2}\right)}{\sin\left(\frac{A}{2}\right)} \]

3. **Calculate \(A + D\):**
\[ A + D = 60° + 30° = 90° \]

4. **Substitute into the Formula:**
Now substitute \(A + D\) and \(A\) into the formula:
\[ n = \frac{\sin\left(\frac{90°}{2}\right)}{\sin\left(\frac{60°}{2}\right)} \]

5. **Calculate the Angles:**
- \(\frac{90°}{2} = 45°\)
- \(\frac{60°}{2} = 30°\)

6. **Find the Sine Values:**
- \(\sin(45°) = \frac{1}{\sqrt{2}}\)
- \(\sin(30°) = \frac{1}{2}\)

7. **Substitute the Sine Values into the Formula:**
\[ n = \frac{\frac{1}{\sqrt{2}}}{\frac{1}{2}} = \frac{1}{\sqrt{2}} \times 2 = \frac{2}{\sqrt{2}} = \sqrt{2} \]

8. **Conclusion:**
The refractive index of the prism should be less than or equal to \(\sqrt{2}\).

### Final Answer:
The refractive index of the prism should be \( n \leq \sqrt{2} \).