If entire Young's double-slit experiment set-up is immersed in water, then

Options

A. fringe width will remain unaffected
B. fringe width will increase
C. fringe width will decrease
D. experiment cannot be performed in water.

Explanation

To solve the problem regarding the effect of immersing the entire Young's double-slit experiment setup in water on the fringe width, we can follow these steps:

### Step 1: Understand Fringe Width
Fringe width (β) is defined as the distance between two consecutive bright or dark fringes in the interference pattern. The formula for fringe width is given by:
\[ \beta = \frac{\lambda D}{d} \]
where:
- \(\lambda\) = wavelength of light used
- \(D\) = distance from the slits to the screen
- \(d\) = distance between the two slits

### Step 2: Effect of Immersing in Water
When the entire setup is immersed in water, the refractive index of water (\(μ\)) affects the wavelength of light. The wavelength of light in a medium is given by:
\[ \lambda' = \frac{\lambda_0}{μ} \]
where:
- \(\lambda_0\) = wavelength of light in air (or vacuum)
- \(μ\) = refractive index of the medium (for water, \(μ \approx 1.33\))

### Step 3: Substitute Wavelength in the Fringe Width Formula
When the setup is in water, the new wavelength (\(\lambda'\)) becomes:
\[ \lambda' = \frac{\lambda_0}{μ} \]
Substituting this into the fringe width formula gives:
\[ \beta' = \frac{\lambda' D}{d} = \frac{\left(\frac{\lambda_0}{μ}\right) D}{d} = \frac{\lambda_0 D}{μ d} \]

### Step 4: Relate New Fringe Width to Original Fringe Width
Now, we can relate the new fringe width (\(\beta'\)) to the original fringe width (\(\beta\)):
\[ \beta' = \frac{\beta}{μ} \]
This shows that the new fringe width is the original fringe width divided by the refractive index of water.

### Step 5: Conclusion
Since \(μ > 1\) for water, it follows that:
\[ \beta' < \beta \]
This means the fringe width decreases when the setup is immersed in water.

### Final Answer
The fringe width decreases when the entire Young's double-slit experiment setup is immersed in water.

---