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A light ray is incident on a glass sphere at angle of incidence $60^{\circ}$ as shown. then the total deviation after two refraction is :

$(a)\;30^{\circ} \\ (b)\;90^{\circ} \\ (c)\;60^{\circ} \\ (d)\;20^{\circ} $

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Applying Snell's law
$1 \sin 60^{\circ}= \sqrt 3 \sin r$
$\qquad => r =30^{\circ}$
From symmetry $r'=r=30^{\circ}$
Again applying snell's law at second surface $1 \sin e =\sqrt 3 \sin r$
$=> e=60^{\circ}$
Deviation at first surface $=i-r=60^{\circ}-30^{\circ}= 30^{\circ}$
Deviation at second surface $=e-r=60^{\circ}-30^{\circ}= 30^{\circ}$
$\therefore $ total deviation $=60^{\circ}$
Hence c is the correct answer.
answered Feb 11, 2014 by meena.p

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