Eduprobe
Question:
In a Young's double slit experiment, the slit separation d is 0.3mm and the screen distance D is 1m. A parallel beam of light of wavelength 600nm is incident on the slits at angle α as shown in figure. On the screen, the point O is equidistant from the slits and distance PO is 11.0mm. Which of the following statement(s) is/are correct?
For α=0.36π degree, there will be destructive interference at point P.
For α=0.36π degree, there will be destructive interference at point O.
Fringe spacing depends on α.
For α=0, there will be constructive interference at point P.
Solution:
Correct option is B. For α=0.36π degree, there will be destructive interference at point P. Δx=dsin α + dsin θ, α: small anglesin θ ≈ tan θ = y/b Δx=dα + dy/D (1) α=0 ∴ Δx=dy/D=0.3 × 11/1000=33 × 10⁻⁴mm Δx in terms of λ=33 × 10⁻⁴/600 × 10⁻⁶; λ=11λ/2 as Δx=(2n-1;)λ/2 There will be destructive interference (2) Δx=0.3mm × 0.36π × π/180 + 0.3mm × 11mm/1000=39 × 10⁻⁴mm 39 × 10⁻⁴=(2n-1) × 600 × 10⁻⁹ × 10³ 2n=7 There will be destructive interference (3) Δx=3mm × 0.36π × π/180 + 0=600nm 600nm=nλ n=1 constructive interference (4) Fringe width does not depend on α.