A small lamp is hung at a height of 8 feet above the centre of a round table of diameter $16\ feet$. The ratio of intensities of illumination at the centre and at points on the circumference of the table will be

Question

Dr. Abubacker · Accepted Answer

(c) Illuminance at $A,\ I_{A} = \frac{L}{h^{2}}$
Illuminance at $B,\ I_{B} = \frac{L}{\sqrt{\left( h^{2} + r^{2} ight)^{2}}}\cos	heta$
$= \frac{Lh}{\left( r^{2} + h^{2} ight)^{3/2}}$
$	herefore\frac{I_{A}}{I_{B}} = \left( 1 + \frac{r^{2}}{h^{2}} ight)^{3/2} = \left( 1 + \frac{8^{2}}{8^{2}} ight)^{3/2} = 2^{3/2} = 2\sqrt{2}:1$

Q. A small lamp is hung at a height of 8 feet above the centre of a round table of diameter $16\ feet$. The ratio of intensities of illumination at the centre and at points on the circumference of the table will be

Explanation

Reviewed by Dr. Abubacker

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