JEE Main 2021 · 24 February · evening · Single correct · +4 / −1
If the source of light used in a Young's double slit experiment is changed from red to violet :
- (a) the fringes will become brighter.
- (b) the intensity of minima will increase.
- (c) consecutive fringe lines will come closer.
- (d) the central bright fringe will become a dark fringe.
Answer and solution
Answer (c) consecutive fringe lines will come closer.
Solution
Physics sir · 4 steps
Fringe width goes as λ, and violet has a shorter wavelength than red, so the fringes squeeze together.
- Fringe width. The gap between two consecutive bright (or dark) fringes is β = (λ D)/d. Here D is the slit-to-screen distance and d is the slit separation.
β = (λ D)/d ⇒ β ∝ λ
- Red to violet. Red light is about 700 nm and violet is about 400 nm. With D and d unchanged, β drops to roughly 400/700 ≈ 0.57 of its old value.
- Other options. Brightness and the intensity at the minima depend on the slit intensities, not on λ. With equal slits, the minima stay at zero. The centre still has zero path difference for every wavelength, so it stays bright.
- So. The fringe width shrinks and consecutive fringes come closer, which is option (c).
The idea to keep. Fringe width β = λ D/d. Changing the colour changes only the spacing. The centre is always bright, because the path difference there is zero for every wavelength.
Answer from the NTA final answer key. Solution by PrepWiser.