Explanation

(b) Since, no force is present along the surface of plane so, momentum conservation principle for ball is applicable along the surface of plate.
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$mv\sin{\theta_{1} = mv_{1}\sin\theta_{2}}$
Or $v\sin{\theta_{1} = v_{1}\sin\theta_{2}}$
$e = \frac{v_{1}\cos\theta_{2}}{v\cos\theta_{1}} = \frac{v_{1}\cos\theta_{2}}{v\cos\theta_{\ }}$
$\therefore\ v_{1}\cos{\theta_{2} = ev\cos\theta_{\ }}$
$\therefore\ \ \frac{v_{1}\sin\theta_{2\ }}{v_{1}\cos\theta_{2}} = \frac{v\sin\theta_{\ }}{ev\ \cos\theta_{\ }} = \frac{\tan\theta_{\ }}{e}$
$\therefore\ \tan\theta_{\ } = \frac{\tan\theta}{e}$
$\therefore\ \theta_{2} = \tan^{- 1}\left( \frac{\tan\theta}{e} \right)$