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A plane wave of monochromatic light falls normally on a uniform thin film of oil which covers glass plate. The wavelength of source can be varied continuously. Complete destructive interference is observed for λ=5000A0 and λ=7000A0 and for no other wavelength in between. If μ of oil 1.3 and that of glass is 1.5, the thickness of the film will be

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a

6.738×10−5cm

b

5.7×10−5cm

c

4×10−5cm

d

2.8×10−5cm

answer is A.

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Detailed Solution

In this case, both the rays suffer a phase change of 1800 and the condition for destructive interference is 2nd=(m+12)λ1 2nd=(m+32)λ2 ∴m+12m+32=λ2λ1=50007000=57 And d=(m+12)λ12n=2.5×70002×1.3 =6738A0= 6.738×10−5cm

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A plane wave of monochromatic light falls normally on a uniform thin film of oil which covers glass plate. The wavelength of source can be varied continuously. Complete destructive interference is observed for λ=5000A0 and λ=7000A0 and for no other wavelength in between. If μ of oil 1.3 and that of glass is 1.5, the thickness of the film will be