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Figure shows that E has the same value f...

Figure shows that E has the same value for all points is front fo an infinitely charged sheet. Is this reasonable? One might think that the field should be stronger near the sheet because the charges are so much closer.

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It is clear form the diagram that the components perpendicular to normal to plate will cancel each other and along the normal `dE cos theta`, they will get added. As the distance decreases, dE increases but `cos theta` also decreases in such a way that `dE cos theta` remain constant for all positions.

It can be observed that near an infinite sheet, electric fields is constant everywhere.
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