A double slit interference experiment experiment is carried out in air and the entire arrangement is dipped in water, As a result

Options

A. The fringe width decreases
B. The fringe width increases
C. The fringe width remains unchanged
D. Fringe pattern disappears

Answer

To solve the problem regarding the effect of dipping the double slit interference experiment in water, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Fringe Width**:
The fringe width (β) in a double slit interference experiment is given by the formula:
\[ \beta = \frac{\lambda D}{d} \]
where:
- \( \lambda \) = wavelength of light used
- \( D \) = distance from the slits to the screen
- \( d \) = distance between the slits

2. **Identify Changes When Dipping in Water**:
When the entire setup is dipped in water, the distance \( D \) and the slit separation \( d \) remain unchanged. The only parameter that changes is the wavelength \( \lambda \) of the light used.

3. **Effect of Medium on Wavelength**:
The wavelength of light in a medium is related to the refractive index (μ) of that medium. The relationship can be expressed as:
\[ \lambda' = \frac{\lambda}{\mu} \]
where:
- \( \lambda' \) = wavelength in the new medium (water)
- \( \lambda \) = wavelength in air
- \( \mu \) = refractive index of the medium

4. **Refractive Index of Air and Water**:
The refractive index of air (approximately 1) is less than that of water (approximately 1.33). Therefore, when light enters water, its wavelength decreases:
\[ \lambda' < \lambda \]

5. **Impact on Fringe Width**:
Since the fringe width is directly proportional to the wavelength, a decrease in wavelength will result in a decrease in fringe width:
\[ \beta' = \frac{\lambda' D}{d} < \frac{\lambda D}{d} = \beta \]
Thus, the fringe width decreases when the setup is submerged in water.

6. **Conclusion**:
The final conclusion is that the fringe width decreases when the double slit interference experiment is conducted in water compared to when it is conducted in air.

### Final Answer:
The fringe width decreases when the entire arrangement is dipped in water.