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This page says illuminance is $$E=\frac{I}{L^2} cos \space \alpha$$

This page does something similar, but it ignores the $cos \space \alpha$ factor. Which is the correct formula?

Note: I don't have a physics background. I was looking at optimization problems in Calculus (which is why I came across the first page).

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2 Answers 2

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A physical formula always applies to a given situation, and it is important to first check whether your situation matches the one this formula is meant for.

The formula without the $\cos \alpha$ term is meant for a situation where the light hits the surface in a right angle. It's a special case of the more general formula, using $\alpha = 0°$ (because then $\cos \alpha$ is 1).

Both pages you linked describe the same situation, one where this isn't true, so the $\cos \alpha$ term is needed.

Nitpicking addition:

The $E=\frac{I}{L^2}\cos\alpha$ formula applies to angles between -90° and 90°, otherwise you'd get negative illuminations (physical nonsense) out of the formula.

Instead the physically correct result would be 0, as a surface pointing away from a light source gets no light at all.

You see, even the "general" formula still has its limitations, being applicable only under specific circumstances.

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  • $\begingroup$ I don't think the second page linked used the formula correctly. Both pages were asking essentially the same question, but the second page didn't take into account the different angle of the table's surface from the direction of incident light, at the table's edge. $\endgroup$ Sep 1, 2022 at 19:56
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I believe the first formula is the correct illuminance. It takes into account the angle of the table's surface. The second definition seems to be for luminance or something similar. See this page, for example.

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  • $\begingroup$ As it’s currently written, your answer is unclear. Please edit to add additional details that will help others understand how this addresses the question asked. You can find more information on how to write good answers in the help center. $\endgroup$
    – Community Bot
    Aug 29, 2022 at 8:10

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