A thin transparent sheet is placed in from of a Young's double slit. The fringe width will

Options

A. increases
B. decrease
C. remain same
D. become nonuniform.

Answer

To solve the question regarding the effect of placing a thin transparent sheet in front of a Young's double slit on the fringe width, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Fringe Width Formula**:
The fringe width (β) in a Young's double slit 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 the Effect of the Transparent Sheet**:
When a thin transparent sheet is placed in front of the double slit, it introduces an additional optical path length due to the refractive index of the material. This causes a shift in the fringe pattern.

3. **Analyze the Impact on Fringe Width**:
The fringe width (β) is determined by the parameters \( \lambda \), \( D \), and \( d \). The introduction of the thin transparent sheet does not change these parameters; it only affects the phase of the light waves reaching the screen.

4. **Conclude the Effect on Fringe Width**:
Since the fringe width depends only on the wavelength, the distance to the screen, and the slit separation, and not on the optical path length introduced by the sheet, the fringe width remains unchanged.

5. **Final Answer**:
Therefore, the fringe width will remain the same after placing the thin transparent sheet in front of the Young's double slit.

### Conclusion:
The correct option is that the fringe width remains the same.

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