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Q.

Two ideal slits S1 and S2 are at a distance d apart, and illuminated by light of wavelength λ passing through an ideal source slit S placed on the line through S2 as shown. The distance between the planes of slits and the source slit is D. A screen is held at a distance D from the plane of the slits. The minimum value of d for which there is darkness at O is

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a

3λD2

b

λD

c

λD2

d

3λD

answer is C.

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Detailed Solution

Δx=λ2 SS1+S1O−(SO)=λ22D2+d2−2D=λ22D1+d22D2−1=λ2d=λD2
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Two ideal slits S1 and S2 are at a distance d apart, and illuminated by light of wavelength λ passing through an ideal source slit S placed on the line through S2 as shown. The distance between the planes of slits and the source slit is D. A screen is held at a distance D from the plane of the slits. The minimum value of d for which there is darkness at O is