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Question

White light may be considered to be a mixture of wavelengths λ ranging between 3900 ˚A and 7800 ˚A. An oil film of thickness 10000 ˚A is examined normally by reflected light. If μ=1.4 , then the film appears bright for-

A
4308 ˚A, 5091 ˚A, 6222 ˚A
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B
4000 ˚A, 5091 ˚A, 5600 ˚A
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C
4667 ˚A,6222 ˚A, 7000 ˚A
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D
4000 ˚A, 4667 ˚A, 5600 ˚A, 7000 ˚A
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Solution

The correct option is A 4308 ˚A, 5091 ˚A, 6222 ˚A
Given, μ=1.4 ; t=10000 ˚A

In, interference due to reflected light, the film appears bright when the path difference,

2μtcosr= odd multiple of λ2

2μt cosr=(2n1)λ2

where n=1,2,3...

λ=4μ t cosr(2n1)

=4×1.4×10000×1010×cos0(2n1)

=56000(2n1) ˚A

For, n=1,2,3,...

λ=56000 ˚A, 18666 ˚A, 8000 ˚A, 5091 ˚A, 4308 ˚A,3733 ˚A,...

The wavelength which are not within specified range are to be refracted.

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, (A) is the correct answer.

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