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(C) Let the height of the source above the table be $h$. Let the source be at a horizontal distance $x$ from the point on the table directly below it.

Vedclass · Accepted Answer

$E \propto \frac{1}{r^3}$

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(C) Let the height of the source above the table be $h$. Let the source be at a horizontal distance $x$ from the point on the table directly below it. The distance $r$ from the source to the point is $r = \sqrt{x^2 + h^2}$. The illuminance $E$ at a point on a surface is given by $E = \frac{I \cos 	heta}{r^2}$,where $I$ is the luminous intensity of the source and $	heta$ is the angle between the normal to the surface and the direction of light. Here,$\cos 	heta = \frac{h}{r}$. Substituting this,we get $E = \frac{I h}{r^3}$. Since $I$ and $h$ are constants,$E \propto \frac{1}{r^3}$.

$A$ point source of light moves in a straight line parallel to a plane table. Consider a small portion of the table directly below the line of movement of the source. The illuminance $E$ at this portion varies with its distance $r$ from the source as:

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