In a double slit experiment, when light of wavelength 400 nm was used, the angular width of the first minima formed on a screen placed 1 m away, was found to be `0.2^(@)`, what will be the angular width of the first minima, if the entire experimental apparatus is immersed in water ? `(mu_("water")=4//3)`

Options

A. `0.1^(@)`
B. `0.266^(@)`
C. `0.15^(@)`
D. `0.05^(@)`

Explanation

To solve the problem, we need to determine the angular width of the first minima in a double slit experiment when the entire apparatus is immersed in water.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- We are given the angular width of the first minima in air (or vacuum) as \( \theta = 0.2^\circ \).
- The wavelength of light used is \( \lambda = 400 \, \text{nm} \).
- The refractive index of water is given as \( \mu_{\text{water}} = \frac{4}{3} \).

2. **Formula for Angular Width**:
- The angular width of the first minima in a double slit experiment can be expressed as:
\[ \theta = \frac{\lambda}{d} \]
- Where \( d \) is the distance between the slits.

3. **Effect of Medium on Wavelength**:
- When the apparatus is immersed in water, the effective wavelength of light changes. The new wavelength \( \lambda' \) in water is given by:
\[ \lambda' = \frac{\lambda}{\mu} \]
- Thus, in water:
\[ \lambda' = \frac{400 \, \text{nm}}{\frac{4}{3}} = 400 \times \frac{3}{4} = 300 \, \text{nm} \]

4. **Calculating New Angular Width**:
- The new angular width \( \theta' \) in water can be calculated using the modified wavelength:
\[ \theta' = \frac{\lambda'}{d} \]
- Since \( d \) remains the same, we can relate the angular widths in air and water:
\[ \theta' = \frac{\lambda'}{d} = \frac{\lambda}{\mu d} = \frac{\theta}{\mu} \]
- Substituting the values:
\[ \theta' = \frac{0.2^\circ}{\frac{4}{3}} = 0.2^\circ \times \frac{3}{4} = 0.15^\circ \]

5. **Final Result**:
- Therefore, the angular width of the first minima when the apparatus is immersed in water is:
\[ \theta' = 0.15^\circ \]

### Summary of the Solution:
The angular width of the first minima when the apparatus is immersed in water is \( 0.15^\circ \).