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Let the speed of the electron be $v_{1}$ when it enters the gap between the plates and $v_{2}$ when it leaves the plates.

As the electron only experiences force in the direction perpendicular to the plates, by the conservation of momentum in the direction parallel to the plates, we have

$v_{1}cos(Î±)=v_{2}cos(Î˛)â‡’v_{1}v_{2}â€‹=cosÎ˛cosÎ±â€‹$

The ratio of kinetic energy is given by $(v_{1}v_{2}â€‹)_{2}=(cosÎ˛cosÎ±â€‹)_{2}$

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