A prism of critical angle 45∘ is immersed water of critical angle 50°. The critical angle of prism inside water will be (sin70° =0.94)

Options

A. `70^@`
B. `90^@`
C. `130^@`
D. `100^@`

Explanation

To find the critical angle of a prism immersed in water, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Critical angle of the prism in air, \( C_p = 45^\circ \)
- Critical angle of water, \( C_w = 50^\circ \)

2. **Calculate the Refractive Index of the Prism:**
- The critical angle \( C \) is related to the refractive index \( \mu \) by the formula:
\[ \mu = \frac{1}{\sin C} \]
- For the prism:
\[ \mu_p = \frac{1}{\sin 45^\circ} \]
- Since \( \sin 45^\circ = \frac{\sqrt{2}}{2} \):
\[ \mu_p = \frac{1}{\frac{\sqrt{2}}{2}} = \sqrt{2} \]

3. **Calculate the Refractive Index of Water:**
- The refractive index of water can be calculated using its critical angle:
\[ \mu_w = \frac{1}{\sin 50^\circ} \]

4. **Calculate the Refractive Index of the Prism with respect to Water:**
- The refractive index of the prism with respect to water is given by:
\[ \mu_{pw} = \frac{\mu_p}{\mu_w} \]
- Substituting the values:
\[ \mu_{pw} = \frac{\sqrt{2}}{\frac{1}{\sin 50^\circ}} = \sqrt{2} \cdot \sin 50^\circ \]

5. **Calculate the Critical Angle in Water:**
- The critical angle \( C' \) in water can be calculated using:
\[ \sin C' = \frac{1}{\mu_{pw}} = \frac{1}{\sqrt{2} \cdot \sin 50^\circ} \]
- Now, we know that \( \sin 50^\circ \) can be approximated from the given information, but we can also calculate it using the known sine values. Using \( \sin 70^\circ = 0.94 \):
\[ \sin 50^\circ \approx \sin(90^\circ - 40^\circ) = \cos 40^\circ \approx \sin 50^\circ \]
- Thus, we can calculate \( C' \):
\[ \sin C' = \frac{2 \sin 50^\circ}{\sqrt{2}} = \sin 70^\circ \]
- Therefore, \( C' = 70^\circ \).

6. **Conclusion:**
- The critical angle of the prism inside water is \( 70^\circ \).

### Final Answer:
The critical angle of the prism inside water is \( 70^\circ \).