Question

Find the least distance from the central maximum where the bright fringes due to both the wavelengths coincide.

Hint:

For fringe coincidence in double slit interference, the condition is that the fringe widths for both wavelengths must be the same.

Answer 1

The condition for bright fringes to coincide for two different wavelengths is: \[ \frac{m_1 \lambda_1}{d} = \frac{m_2 \lambda_2}{d} \] Where: - \( m_1 \) and \( m_2 \) are the fringe orders for the two wavelengths, - \( \lambda_1 = 600 \, \text{nm} \) and \( \lambda_2 = 480 \, \text{nm} \). Solving for \( m \), we find the least value where the bright fringes coincide. The distance will be found similarly to the earlier calculation, using the conditions for interference.