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, we need to find the wavelength of light (λ₂) for which the first order dark fringe coincides with the position of the first order bright fringe of the given wavelength (λ₁ = 600 nm).

### Step-by-Step Solution:

1. **Understand the Interference Pattern**:
- For a double-slit interference pattern, the position of bright fringes is given by:
\[
y_n = \frac{n \lambda d}{D}
...