For an optical arrangement as depicted in the figure, the distance $D$ is significantly greater than the slit separation $d$ . Assume $d$ is set to the minimum value required to produce a dark fringe at point $O$ . Determine the fringe width of the interference pattern.

Question

For an optical arrangement as depicted in the figure, the distance

D

is significantly greater than the slit separation

d

. Assume

d

is set to the minimum value required to produce a dark fringe at point

O

. Determine the fringe width of the interference pattern.
For an optical arrangement as depicted in the figure, the distance D is significantly greater than the slit separation

For an optical arrangement as depicted in the figure, the distance D is significantly greater than the slit separation

Quantrex Academy · Accepted Answer

Correct answer: B. 4d

Path difference at point O is Δ x_O = (S_0 S_1 + S_1 O) - (S_0 S_2 + S_2 O) For D d , the distances are: S_0 S_1 = S_1 O = D^2 + d^2 D + (d^2)/(2D) S_0 S_2 = S_2 O = D Δ x_O = 2(D + (d^2)/(2D)) - 2D = (d^2)/(D) For a dark fringe at O with minimum d , Δ x_O = (λ)/(2) (d^2)/(D) = (λ)/(2) λ = (2d^2)/(D) The fringe width β on the screen for sources separated by d at distance D is β = (λ D)/(d) β = ((2d^2)/(D)) (D)/(d) = 2d

For an optical arrangement as depicted in the figure, the distance...

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