A plane wave of monochromatic light falls normally on a uniform thin film of oil which covers a glass plate. The wavelength of source can be varied continuously. Complete destructive interference is observed for l = 5000 Å and l = 7000 Å and for no other wavelength in between. If m of oil is 1.3 and that of glass is 1.5, the thickness of the film will be
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a
6.738 × 10-5 cm
b
5.7 × 10-5 cm
c
4 × 10-5 cm
d
2.8 × 10-5 cm
answer is A.
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Detailed Solution
In this case, both the rays suffer a phase change of 180∘ and the condition for destructive interference is: 2nd=(m+12)λ12nd=(m+32)λ2,∴m+12m+32=λ2λ1=50007000=57and d=(m+12)λ12n=2.5×70002×1.3=6738Å=6.738×10-5cm.