>>I still feel rather uncomfortable with this comment. Because there is >>some truth in it. By this I mean the way infinitesimals are _actually_ >>done in i.e. physics. I have an example of this and would be glad if >>someone feels like scrutinizing it. It's in the following document: >>http://hdebruijn.soo.dto.tudelft.nl/jaar2006/RobertLow.PDF >>The problem is in the assumption at the bottom of page 1, where it is >>assumed that two angles are 90 degrees, _before_ the limit is taken, >>while this can be motivated only _after_ the limit has been taken.
>>It seems weird, but I don't know how to arrive at the result in another >>manner. I would be thankful if somebody points me out how to accomplish >>the same, but without being "sloppy" in this way.
> I'll just consider the 2-d case, where everything lies > in a plane. I think you're computing the light intensity > at B due to a unit source at F, so that's what > the following will work with. You can recover the full > 3-d case by rotating about AF if you want to.
Bunch of stuff deleted.
I should probably have mentioned that I don't think any mathematician would bat an eyelid at what was essentially your argument namely: Let dS be an element of surface at B tangent to a sphere centred at F. Then the projection of dS to the image plane has area dS/cos(alpha), so the intensity at B is just cos(alpha)/(4 pi R^2).
Or even shorter: the intensity vector E at B is given by 1/(4pi R^2) * the unit radial vector, so the component perpendicular to that is just the dot product of E with the perpendicular to the image plane, which is the same as above.
(And I belatedly realised that you were using 1/2pi there so that the total flux through the image plane would be 1, which I would call a source of strength 2, rather than 1.)
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