Question

A cylindrical shape hall has height of 4 m. What should be the radius of hall so that when bulb on the ceiling is switched on, same amount of light falls on floor as well as on walls? [Radius of hall is in meters] (Take $\sqrt{3}=1.73$) Write upto two digits after the decimal point.

Answer 1

The solid angle formed by the bulb at the base is given by $\omega =2\pi (1-cos\theta )$
The total solid angle downwards the bulb is $2\pi$. For equal amount of light between the base and the wall, the solid angle made by the base should be equal to $\pi$. So,

$\pi =2\pi (1-cos\theta )$

$\theta ={60}^{\circ }$

$\tan {60}^{\circ }=\frac{R}{H}=R=H\sqrt{3}=4\sqrt{3}=6.92$