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White light may be considered to be a mixture of waves with \lambda ranging between 3900 \mathrm{~A}^{0} and 7800 \mathrm{~A}^{0}.An oil film of thickness 10,000 A^{0} is examined normally by a reflected light. If \mu=1.4, then the film appears bright for

Option: 1

4308 \mathrm{~A}^{0}, 5091 \mathrm{~A}^{0}, 6222 \mathrm{~A}^{0}


Option: 2

4000 \mathrm{~A}^{0}, 5091 \mathrm{~A}^{0}, 5600 \mathrm{~A}^{0


Option: 3

4667 \mathrm{~A}^{0}, 6222 \mathrm{~A}^{0}, 7000 \mathrm{~A}^{0}


Option: 4

4000 \mathrm{~A}^{0}, 4667 \mathrm{~A}^{0}, 5600 \mathrm{~A}^{0}, 7000 \mathrm{~A}^{0}


Answers (1)

best_answer

The film appears bright when the path difference

\mathrm{( 2 \mu \mathrm{t} \cos r) } is equal to odd multiple of \mathrm{\lambda / 2 },
\mathrm{i.e., \quad 2 \mu t \cos r=(2 n-1) \frac{\lambda}{2}}
\mathrm{where \, \mathrm{n}=1,2,3 \ldots}
\mathrm{\therefore \quad \lambda=\frac{4 \mu \mathrm{t} \cos r}{(2 \mathrm{n}-1)}}
\mathrm{=\frac{4 \times 1.4 \times 10,000 \times 10^{-10} \times \cos 0}{(2 \mathrm{n}-1)}=\frac{56000}{(2 \mathrm{n}-1)} \mathrm{A}^{0}}

\mathrm{\therefore \lambda=56000 \mathrm{~A}^{0}, 1866 \mathrm{~A}^{0}, 11200 \mathrm{~A}^{0}, 8000 \mathrm{~A}^{0}, 6222 \mathrm{~A}^{0}, 5091 \mathrm{~A}^{0},4308 A^{0}, 3733 A^{0}}.

The wavelengths, which are not within specified range, are to be neglected.

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Anam Khan

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