State the approximate value of the critical angle for (a) glass-air surface
(b) water-air surface.

Answer

To find the approximate values of the critical angle for the glass-air surface and the water-air surface, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Critical Angle**:
The critical angle is the angle of incidence above which total internal reflection occurs. It can be calculated using the formula:
\[ \sin(I_C) = \frac{1}{\mu} \]
where \( I_C \) is the critical angle and \( \mu \) is the refractive index of the medium with respect to air.

2. **Determine the Refractive Index for Glass**:
The refractive index of glass with respect to air is approximately \( \mu_{glass} = \frac{4}{3} \).

3. **Calculate the Critical Angle for Glass**:
Using the formula for the critical angle:
\[ \sin(I_C) = \frac{1}{\mu_{glass}} = \frac{1}{\frac{4}{3}} = \frac{3}{4} \]
Now, calculate \( I_C \):
\[ I_C = \sin^{-1}\left(\frac{3}{4}\right) \]
Using a calculator, we find:
\[ I_C \approx 48.59^\circ \]
Thus, the approximate value of the critical angle for the glass-air surface is **49 degrees**.

4. **Determine the Refractive Index for Water**:
The refractive index of water with respect to air is approximately \( \mu_{water} = \frac{3}{2} \).

5. **Calculate the Critical Angle for Water**:
Using the formula for the critical angle:
\[ \sin(I_C) = \frac{1}{\mu_{water}} = \frac{1}{\frac{3}{2}} = \frac{2}{3} \]
Now, calculate \( I_C \):
\[ I_C = \sin^{-1}\left(\frac{2}{3}\right) \]
Using a calculator, we find:
\[ I_C \approx 41.81^\circ \]
Thus, the approximate value of the critical angle for the water-air surface is **42 degrees**.

### Final Answer:
- (a) The approximate value of the critical angle for the glass-air surface is **49 degrees**.
- (b) The approximate value of the critical angle for the water-air surface is **42 degrees**.