A parallel beam of white light falls from air on a thin film whose refractive index is $\sqrt{3}$ . The medium on both sides of the film is air. The angle of incidence is 60°. Find the minimum film thickness if reflected light is most intense for $λ = 600 nm .$

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150 nm

200 nm

100 nm

300 nm

answer is C.

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Detailed Solution

$\sin 60^{0} = \sqrt{3} \sin r \Rightarrow r = 30^{0}$
The optical path difference between R₁ and R₂ is given by
$\begin{array}{l} Δx = 2 μtsecr - 2 t tanrsini \\ = 2 \sqrt{3} (tsec 30^{0}) - 2 t \tan 30^{0} . \sin 60^{0} = 3 t \end{array}$
$∴$ For constructive interference, we have $3 t = \frac{λ}{2}; \frac{3 λ}{2} . ....$
For minimum t $3 t = \frac{λ}{2}$
$\Rightarrow t = \frac{λ}{6} = 100 nm .$