Question

A 60 watt bulb is hung over the center of a table $4' \times 4'$ at a height of 3'. The ratio of the intensities of illumination at a point on the centre of the edge and on the corner of the table is

• A. $(17/13)^{3/2}$
• B. 2 / 1
• C. 17 / 13
• D. 5 / 4

Answer 1

Answer: (A)

$(17/13)^{3/2}$

Answer 2

The illuminance at A is

$I_{A} = \frac{L}{(\sqrt{13})^{2}} \times \cos\theta_{1} = \frac{L}{13} \times \frac{3}{\sqrt{13}} = \frac{3L}{(13)^{3/2}}$

The illuminance at B is

$I_{B} = \frac{L}{(\sqrt{17})^{2}} \times \cos\theta_{2} = \frac{L}{17} \times \frac{3}{\sqrt{17}} = \frac{3L}{(17)^{3/2}}$

$\therefore$ $\frac{I_{A}}{I_{B}} = \left( \frac{17}{13} \right)^{3/2}$