In many instances, I have noticed that it is given that the aperture is less than the radius of curvature for a spherical mirror. Why is this given like that?
Why is it desired to have an aperture of a spherical mirror to be less than the radius of curvature?
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1$\begingroup$ The reason us not given in my textbook. $\endgroup$– alvinCommented Oct 26, 2015 at 15:20
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$\begingroup$ Had not the aperture been smaller than the radius of curvature, all the rays parallel to the principal axis, wouldn't converged to a single point which we call focus. That is the reason for this approximation. $\endgroup$– user36790Commented Oct 26, 2015 at 15:49
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$\begingroup$ It's okay. But I strongly refer to switch over your book & start reading some good book. $\endgroup$– user36790Commented Oct 26, 2015 at 16:08
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1$\begingroup$ @user36790 Why did you post an answer as a comment? Just post it as an answer. $\endgroup$– DanielSankCommented Oct 26, 2015 at 16:42
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2$\begingroup$ @user36790 "start reading some good book" is terrible advice, clearly OP does not know that his/her book is "not good" to begin with. How is OP supposed to know what a "good book" is? $\endgroup$– Ryan UngerCommented Oct 26, 2015 at 23:24
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1 Answer
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Spherical mirrors do not focus parallel light rays to a single focal point. The focus actually lies on a surface called a caustic. Wolfram have a nice demonstration of this here.
Light rays close to the centre of the mirror, i.e. the region where the mirror is only slightly angled away from the vertical, do come to a single focal point to a good approximation. This is known as the paraxial approximation. The point of using an aperture much smaller that the radius of the mirror is to restrict the incoming light to a region where rays do (almost) come to a single focal point.
answered Oct 26, 2015 at 17:57