Question

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

• A. 1 : 1
• B. 2 : 1
• C. $2\sqrt{2}:1$
• D. 3 : 2

Answer 1

Answer: (C)

$2\sqrt{2}:1$

Answer 2

Illuminance at A, $I_{A} = \frac{L}{h^{2}}$

Illuminance at B, $I_{B} = \frac{L}{\sqrt{(h^{2} + r^{2})^{2}}}\cos\theta = \frac{Lh}{(r^{2} + h^{2})^{3/2}}$

$\therefore\frac{I_{A}}{I_{B}} = \left( 1 + \frac{r^{2}}{h^{2}} \right)^{3/2} = \left( 1 + \frac{8^{2}}{8^{2}} \right)^{3/2} = 2^{3/2} = 2\sqrt{2}:1$