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Focusing surfaces

Published online by Cambridge University Press:  01 August 2016

Hassan Azad ,
Abdallah Laradji  and
Asghar Qadir
Hassan Azad
Affiliation:
Department of Mathematical Sciences, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia
Abdallah Laradji
Affiliation:
Department of Mathematical Sciences, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia
Asghar Qadir
Affiliation:
Centre for Advanced Mathematics and Physics, National University of Science and Technology, Islamabad, Pakistan
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Extract

In standard textbooks (e.g. [1, p. 877]) as well as in Encylopaedia Britannica [2, Vol. 13, p. 611], one finds variants of the following statement:

In spherical mirrors, rays parallel and very close to the principal axis are all reflected through a single point.

This statement is actually false, and can only be understood in the following sense: It is true only up to a linear approximation, and in fact, as soon as a mirror focuses parallel rays, it must be a parabolic mirror.

Type
Articles
Information
The Mathematical Gazette , Volume 90 , Issue 519 , November 2006 , pp. 404 - 411
Copyright
Copyright © The Mathematical Association 2006

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References

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