Let ball strikes the plate with speed v. Suppose ${\text{v}}^{\prime }$ is the speed after the collision and $\mathrm{\alpha }$ is the angle of reflection. Parallel component of velocity of the ball remain constant as there is no force parallel to surface.

${\text{v}}^{\prime }\sin \mathrm{\alpha }=\mathrm{v}\sin \mathrm{\theta }$           ...(i)

Velocity of sepration $={{\text{v}}^{\prime }\cos \alpha }^{}$

Velocity approach $=\mathrm{v}\cos \mathrm{\theta }$

$\therefore \mathrm{e}=\frac{{\text{v}}^{\prime }\cos \mathrm{\alpha }}{\mathrm{v}\cos \mathrm{\theta }}$

${\text{v}}^{\prime }\cos \mathrm{\alpha }=\mathrm{e}\mathrm{ }\mathrm{v}\cos \mathrm{\theta }$           ...(ii)

from eq (i) and (ii)

$\tan \mathrm{\alpha }=\frac{\tan \mathrm{\theta }}{\mathrm{e}}$

$\mathrm{\alpha }={\tan }^{-1}\left(\frac{\tan \mathrm{\theta }}{\mathrm{e}}\right)$