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Consider a light ray travelling in air is incident into a medium of refractive index \mathrm{\sqrt{2n}}. The incident angle is twice that of refracting angle. Then, the angle of incidence will be :

Option: 1

\mathrm{\sin^{-1}\left ( \sqrt{n} \right )}


Option: 2

\mathrm{\cos^{-1}\left ( \sqrt{\frac{n}{2}} \right )}


Option: 3

\mathrm{\sin^{-1}\left ( \sqrt{2n} \right )}


Option: 4

\mathrm{2\cos^{-1}\left ( \sqrt{\frac{n}{2}} \right )}


Answers (1)

best_answer

\mathrm{\quad i=2 r}

\mathrm{By \ snell's \ law}\\

\mathrm{1 x \sin i=\sqrt{2 n} \sin r}\\

\mathrm{\sin (2 r)=\sqrt{2 n} \sin r}\\

\mathrm{2 \sin r \cos r=\sqrt{2 n} \sin r}\\

\mathrm{\cos r=\frac{\sqrt{n}}{\sqrt{2}}}\\

\mathrm{r=\cos ^{-1}\left(\sqrt{\frac{n}{2}}\right)} \\

\mathrm{i=2 r=2 \cos ^{-1}\left(\sqrt{\frac{n}{2}}\right)}

Posted by

sudhir.kumar

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