In Young's double slit experiment, if the width of 4th bright firnge is `2xx10^(-2)` cm then the width of 6 th bright fringe will be cm

Options

A. `10^(-2)`
B. `3xx10^(-2)`
C. `2xx10^(-2)`
D. `1.5xx10^(-2)`

Explanation

To solve the problem, we need to understand the concept of fringe width in Young's double slit experiment. The fringe width (β) is given by the formula:

\[ \beta = \frac{\lambda D}{d} \]

where:
- \( \beta \) is the fringe width,
- \( \lambda \) is the wavelength of light used,
- \( D \) is the distance from the slits to the screen,
- \( d \) is the distance between the two slits.

### Step-by-Step Solution:

1. **Understanding Fringe Width**: The fringe width is the distance between two consecutive bright or dark fringes. It is constant for all fringes in Young's double slit experiment.

2. **Given Information**: We know that the width of the 4th bright fringe is \( 2 \times 10^{-2} \) cm.

3. **Independence of Fringe Width**: The fringe width does not depend on the order of the fringe (n). This means that the width of the nth bright fringe is the same as the width of any other nth bright fringe.

4. **Conclusion for 6th Bright Fringe**: Since the fringe width is constant, the width of the 6th bright fringe will also be the same as that of the 4th bright fringe.

5. **Final Answer**: Therefore, the width of the 6th bright fringe is also \( 2 \times 10^{-2} \) cm.

### Summary:
The width of the 6th bright fringe is \( 2 \times 10^{-2} \) cm.

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