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The reflected rays of light are not parallel or coinciding to each other, so they will have a unique solution(point of intersection) but why is that point of intersection half of centre of curvature and why meet on the principal axis?

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    $\begingroup$ This is a good exercise in geometry :) $\endgroup$ Oct 19, 2019 at 6:42

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First of all, this is not exact. Point of intersection is half way of radius only for small mirrors id est, small surfaces of mirrors with big curvatures. First of all, you need to draw geometric situation. If we agree that according to the law of reflection ray must reflect of the mirror as it is reflecting of the plane mirror which is represented by the tangent to the spherical mirror at the point of incidence and that the mirror is small that is, we cut a small surface of a big sphere, then this picture should serve as a proof...enter image description here

If we agree that FE and BF are the same (almost) then we just have to prove that FE is the same as CF. But as you can see, BF is the same as CF. So CF=FE. Point of incidence is B. $\theta$ is the angle of incidence.

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Parallel rays of light are not brought into sharp focus by spherical mirrors. They suffer a defect known as spherical aberration.

Getting a sharp image requires either a parabolic mirror (as commonly seen in Newtonian reflector telescopes) or an aspheric correcting lens in front of the mirror (as in Schmidt-Cassegrain telescopes).

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