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A ray of light is incident on a transparent glass slab of refractive index $1.62$ . If the reflected and refracted rays are mutually perpendiculars, what is angle of incidence?

$(a)\;\tan^{-1} 1.31 \\ (b)\;\tan ^{-1} 1.5 \\ (c)\;\tan ^{-1} 1.62 \\ (d)\;\tan ^{-1} 2.5 $

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Let angle of incidence , angle of reflection and angle of refraction be i, r and r' respectively
as per the question ,
$90-r +90 -r'=90$
=> $r'= 90-i$ (because $i=r$ in case of reflection according to Snell's law )
$1 \sin i =y \sin r$
or $\sin i =y \sin r'$
or $\sin i =y \sin (90-i)$
=> $\tan i =y$
or $i=\tan ^{-1} y$
$\qquad= \tan ^{-1} 1.62$
Hence c is the correct answer.
answered Feb 11, 2014 by meena.p

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