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=dsinα+dsinθ⇒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
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 ?