Question

A bulb of 100 watt is hanging at a height of one meter above the centre of a circular table of diameter 4 m. If the intensity at a point on its rim is $I_{0}$, then the intensity at the centre of the table will be

• A. $I_{0}$
• B. $2\sqrt{5}I_{0}$
• C. $2I_{0}$
• D. $5\sqrt{5}I_{0}$

Answer 1

Answer: (D)

$5\sqrt{5}I_{0}$

Answer 2

The illuminance at B

$I_{B} = \frac{L}{1^{2}}$ .......(i)

and illuminance at point C

$I_{C} = \frac{L\cos\theta}{(\sqrt{5)^{2}}} = \frac{L}{(\sqrt{5)^{2}}} \times \frac{1}{\sqrt{5}}$

$\Rightarrow \mspace{6mu}\mspace{6mu} I_{C} = \frac{L}{5\sqrt{5}}$ ...... (ii)

From equation (i) and (ii)

$I_{B} = 5\sqrt{5}\mspace{6mu} I_{0}$