# Describing the surface of a sphere in Huygens' Principle

$U(P) = \frac {iU(r_0)}{\lambda} \int_{S} \frac {e^{iks}}{s} K(\chi)\,dS$

Where $S$ describes the surface of the sphere, how is the surface of the sphere described?

Sorry if you feel this is quite a simple question, I couldn't find the information anywhere on the internet.

(I'm not entirely sure about the tag either) so any edits would be much appreciated

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Wikipedia reference: en.wikipedia.org/wiki/Huygens%E2%80%93Fresnel_principle – Qmechanic Mar 31 '12 at 19:27
Thanks but I don't think I'd ask a question before looking on wikipedia (it tends to be one of the first places one looks) – ODP Apr 2 '12 at 22:44
My comment is meant as a help for anyone who is interested in the question. – Qmechanic Apr 2 '12 at 23:37

"Describes" is used here like "inscribed"

Note that there is an $S$ underneath the integral sign as well. This means that its a surface integral. The integral is carried out over a surface, analogous to how a line integral is carried out over a path.

$\rm dS$ will be a small area element. In most surface integrals, you can write it as a product of two differentials. For example, on a plane (parallel to $xy$ plane), $\rm dS=\rm dx \rm dy$. For a sphere, $\rm dS=r\rm d\theta \times r\sin\theta\rm d\varphi$.

Question: Are you trying to learn optics via Wikipedia(looking at your previous questions). Wikiepdia is a bad place to learn stuff--its a reference--which means that it assumes you know everything and want to know more :/. I suggest getting a textbook if you are Wikipedia-studying. There also are free online lecture videos and material, like those from MIT or Khan Academy.

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Okay thank you, I'd like to get a book but the best one is unbelievably expensive (that by Hecht) but I will look on MIT and Khan Academy like you suggested, thanks. – ODP Mar 31 '12 at 13:28
Hecht is not a good beginners text. you might try "Fourier optics" by Goodman. If it is wave optics you are trying to learn. – Colin K Mar 31 '12 at 14:56
But regardless of the book you get you will need to understand calculus. You should already be familiar with a surface integral. – Colin K Mar 31 '12 at 14:59
@Olly due to all the dependancies, you may want to ask(on P.SE chat) which order to learn these dependancies. I'd say geometry, calculus, basic curvilinear calculus, ray optics, wave optics, etc. But I'm not too sure, ColinK will probably be able to answer this with book reccomendations. – Manishearth Mar 31 '12 at 15:04
Colin K, did you mean I need to be familiar with a surface integral if I want to begin learning optics? – ODP Mar 31 '12 at 15:45