Flux through an infinite plane due to a point charge

Homework Statement

A point charge q is located a distance d meters from an infinite plane. Determine the electric flux through the plane due to the point charge.
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The Attempt at a Solution

I consider another infinite plane at a distance d in the opposite direction. Now I have infinite cuboid.

The flux through all the surfaces of the cuboid is ## \frac {q } { \epsilon _0} ##.

Since the plane with length d is smaller than the other two planes, the flux through these two planes is negligible in comparison with that due to the other two infinite planes. The other two infinite planes have equal flux. So, the flux through one infinite plane is ## \frac {q } { 2 \epsilon _0} ##.

Is this correct?