In a biprism experiment, the biprism is made of glass (n = 1.5). When the setup is shifted from air to the inside of a still, clear lake water `(n = 4 // 3)` then

Options

A. The fringe pattern gets enlarged
B. The fringe pattern gets shrunk
C. The fringe pattern gets shifted
D. The fringe pattern remains unchanged

Answer

To solve the problem regarding the biprism experiment when the setup is shifted from air to water, we will analyze the changes in fringe width due to the change in the medium.

### Step-by-Step Solution:

1. **Understanding the Setup**:
The biprism creates two coherent sources of light. The fringe width (β) in an interference pattern is influenced by the refractive index of the medium in which the light travels.

2. **Fringe Width in Air**:
The fringe width (d) when the biprism is in air can be expressed as:
\[ d_a = \frac{\lambda}{\mu_g} \cdot \frac{D}{d} \]
where:
- \( \lambda \) = wavelength of light in air,
- \( \mu_g \) = refractive index of glass (1.5),
- \( D \) = distance between the coherent sources,
- \( d \) = distance from the slit to the biprism.

3. **Fringe Width in Water**:
When the setup is shifted to water, the fringe width (d) can be expressed as:
\[ d_w = \frac{\lambda}{\mu_w} \cdot \frac{D}{d} \]
where:
- \( \mu_w \) = refractive index of water (4/3).

4. **Comparing Fringe Widths**:
To compare the fringe widths in air and water, we take the ratio:
\[ \frac{d_w}{d_a} = \frac{\frac{\lambda}{\mu_w} \cdot \frac{D}{d}}{\frac{\lambda}{\mu_g} \cdot \frac{D}{d}} = \frac{\mu_g}{\mu_w} \]

5. **Substituting Values**:
Substituting the values of the refractive indices:
\[ \frac{d_w}{d_a} = \frac{1.5}{\frac{4}{3}} = \frac{1.5 \times 3}{4} = \frac{4.5}{4} = 1.125 \]
This means that the fringe width in water is 1.125 times that in air.

6. **Conclusion**:
Since \( d_w > d_a \), the fringe pattern gets enlarged when the setup is shifted from air to water.

### Final Answer:
The fringe pattern gets enlarged when the biprism setup is shifted from air to the inside of still clear lake water.