The width of fringe is 2 mm on the screen in a double slits experiment for the light of wavelength of 400 nm. The width of the fringe for the light of wavelength 600 nm will be:

Solution

Physics sir · 3 steps

Same slits, same screen, so fringe width just scales with wavelength: 600 is 1.5 times 400.

1. Fringe width. In Young's double slit experiment, the fringe width depends on the wavelength, the slit-to-screen distance D and the slit separation d.

   β = (λ D)/d

2. Take the ratio. Only the light changes, so D and d stay the same and β ∝ λ. That gives β₂/β₁ = λ₂/λ₁ = 600/400 = 1.5.
3. So. β₂ = 1.5 × 2 mm = 3 mm, which is option (d).

The idea to keep. When the setup is unchanged, fringe width goes directly with wavelength. Longer wavelength means wider fringes, so red light spreads the pattern more than violet.

Answer from the NTA final answer key. Solution by PrepWiser.