In Young.s double slit experiment, using monochromatic light, fringes are obtained on a screen placed at some distance from the slits. If the screen is moved by `5 xx 10^(-2)` m towards the slits, the change in the fringe width is `3 xx 10^(-5)` m. If the distance between the two slits is `10^(-3)m`, calculate wavelength of the light used.

Explanation

To solve the problem, we will use the relationship between fringe width, distance to the screen, and wavelength in Young's double-slit experiment.

### Step-by-Step Solution:

1. **Identify Given Values**:
- Distance between the slits, \( D = 10^{-3} \, \text{m} \)
- Change in position of the screen, \( \Delta D = 5 \times 10^{-2} \, \text{m} \)
- Change in fringe width, \( \Delta \beta = 3 \times 10^{-5} \, \text{m} \)
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