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Q.

In a Young’s double slit experiment, the slit separation d is 0.3 mm and the screen distance D is 1 m. A parallel beam of light of wavelength 600 nm 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 11.0 mm. Which of the following statement(s) is/are correct ?

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a

Fringe spacing depends on α

b

For α=0.36π degree, there will be destructive interference at point O.

c

For  α=0, there will be constructive interference at point P.

d

For α=0.36π degree, there will be destructive interference at point P.

answer is D.

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Detailed Solution

Path difference, Δx=dsin⁡α+dsin⁡θ⇒Δx=dα+ydD [∵ both α&θ are small angles ] For α=0 , ⇒Δx=0+11×10−3×0.3×10−31=3.3×10−6m=3300nmConstructive Interference , Δx=nλ , here n should be an integer⇒n=Δxλ=3300600=5.5P is 6 th minima, destructive interference  For α=0.36πdeg , ⇒Δx=0.3×10−3×36×10−2180+0.3×10−3×11×10−31=n6×10−7⇒6×10−7+33×10−7=n6×10−7⇒n=396=6.5 means 7 th minima, destructive interference At point O ,Δx=dα+0=0.3×10−3×36×10−2180=n6×10−7⇒6×10−7=n6×10−7⇒n=1, means 1 st maxima, constructive interference Fringe width does not depend on α​. Fringe width= λDd=6×10−7×13×10−4=2mm
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In a Young’s double slit experiment, the slit separation d is 0.3 mm and the screen distance D is 1 m. A parallel beam of light of wavelength 600 nm 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 11.0 mm. Which of the following statement(s) is/are correct ?