Question

A lamp of luminous intensity $20$ $Cd$ is hanging at a height of $40$ $cm$ from the center of a square table of side $60$ $cm$. The illuminance at the midpoint of the side of the table will be

• A. $125$ lux
• B. $100$ lux
• C. $64$ lux
• D. $32$ lux

Answer 1

Answer: (C)

$64$ lux

Luminous intensity, L = 20 Cd

Distance of source from center of table, h = 40 cm

Distance of center of table to midpoint of side of table = a/2 = 30 cm

Total distance between source and point, d = $\sqrt{(h^2+(a/2{)}^2)}$ = 50 cm

As per attached picture Cos (theta) = 4/5

Lambert's law, $I=LCos\theta /d^2$

$\to I=20\left(4/5\right)/(0.5{)}^2$

$\to I=64lux$

Answer. C) 64 lux