QJEEAdv08Phc557: JEE Advanced 2008 Physics - Class 12 JEEAdv08Phc557 Solution: A light beam is travelling from Region I to Region IV (Refer…

From Snell's laws

${\mu _1}\sin \theta = {\mu _2}\sin {\theta _2}$

Case I : Region I

${n_0}\sin \theta = {{{n_0}} \over 2}\sin \alpha$ ...... (i)

Case II : Region II

${{{n_0}} \over 2}\sin \alpha = {{{n_0}} \over 6}\sin {\theta _c}$ ..... (ii) ( $\therefore$ $\beta = {\theta _c}$ )

Case II : Region III

${{{n_0}} \over 6}\sin {\theta _c} = {{{n_0}} \over 8}\sin 90^\circ$

$\Rightarrow {{{n_0}} \over 6}\sin {\theta _c} = {{{n_0}} \over 8}$ ..... (iii)

From equation (i), (ii) and (iii), we have,

${n_0}\sin \theta = {{{n_0}} \over 8}$

$\Rightarrow \sin \theta = {1 \over 8}$

$\Rightarrow \theta = {\sin ^{ - 1}}\left( {{1 \over 8}} \right)$