In a Young's double-slit experment, the fringe width is `beta`. If the entire arrangement is now placed inside a liquid of refractive index `mu`, the fringe width will become

Options

A. `beta`
B. `beta/mu`
C. `beta/(mu+1)`
D. `beta/(mu-1)`

Explanation

To find the new fringe width when the entire Young's double-slit experiment is placed in a liquid of refractive index \( \mu \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Original Fringe Width**:
The fringe width \( \beta \) in a Young's double-slit experiment is given by the formula:
\[ \beta = \frac{\lambda D}{d} \]
where \( \lambda \) is the wavelength of light in air, \( D \) is the distance from the slits to the screen, and \( d \) is the distance between the slits.

2. **Effect of the Medium**:
When the experiment is placed in a medium with refractive index \( \mu \), the wavelength of light in that medium \( \lambda_m \) can be expressed as:
\[ \lambda_m = \frac{\lambda}{\mu} \]
This means the wavelength of light decreases when it enters a medium with a refractive index greater than 1.

3. **New Fringe Width Calculation**:
The new fringe width \( \beta' \) in the medium can be calculated using the same formula for fringe width, but substituting the new wavelength \( \lambda_m \):
\[ \beta' = \frac{\lambda_m D}{d} = \frac{\left(\frac{\lambda}{\mu}\right) D}{d} \]
Simplifying this gives:
\[ \beta' = \frac{\lambda D}{\mu d} = \frac{\beta}{\mu} \]

4. **Final Result**:
Therefore, the new fringe width \( \beta' \) when the entire arrangement is placed in the liquid is:
\[ \beta' = \frac{\beta}{\mu} \]

### Conclusion:
The fringe width becomes \( \frac{\beta}{\mu} \) when the arrangement is placed in a liquid of refractive index \( \mu \).