Coherent light with wavelength 600nm passes through two very narrow slits and the interference pattern is observed on a screen 3.00 m from the slits. The first order bright fringe is at 4.94 mm from the centre of the central bright fringe. For what wavelength of light will the first order dark fringe be observed at this same point on the screen?

Explanation

To solve the problem step by step, we will use the principles of interference and the relationship between fringe width, wavelength, and distance.

### Step 1: Understand the given data
We have:
- Wavelength of light, \( \lambda = 600 \, \text{nm} = 600 \times 10^{-9} \, \text{m} \)
- Distance from the slits to the screen, \( D = 3.00 \, \text{m} \)
- Distance of the first order bright fringe from the center, \( y = 4.94 \, \text{mm} = 4.94 \times 10^{-3} \, \text{m} \)

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