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Q.

A thin large film having refractive index  μ=32, is placed in front of slits S1 and  S2 of Young's double slit experiment such that its thickness varies according to the equation  t=t0cos25πy4d where y = 0 is taken at  S1. Find the value of t0  such that there is central maxima at P (refer diagram) Assume  D>>d

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a

d2D

b

2d2D

c

d22D

d

d24D

answer is B.

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Detailed Solution

t1=t0cos2⁡0=t0t2=t0cos2⁡5π4d(−d)=t02 For central maxima at PS2P−S1P+(μ−1)t2−t1=0⇒dxd/2D=32−1t0−t02⇒t0=2d2D
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A thin large film having refractive index  μ=32, is placed in front of slits S1 and  S2 of Young's double slit experiment such that its thickness varies according to the equation  t=t0cos25πy4d where y = 0 is taken at  S1. Find the value of t0  such that there is central maxima at P (refer diagram) Assume  D>>d