About 5% of the power of a 100 W light bulb is converted to visible radiation. What is the average intensity of visible radiation
(a) at a distance of 1 m from the bulb?
(b) at a distance of 10 m?
Assume that the radiation is emitted isotropically and neglect reflection.
Power rating of bulb, P = 100 W
It is given that about 5% of its power is converted into visible radiation.
$\therefore$ Power of visible radiation,
$P^{\prime}=\frac{5}{100} \times 100=5 \mathrm{~W}$
Hence, the power of visible radiation is 5W.
(a) Distance of a point from the bulb, d = 1 m
Hence, intensity of radiation at that point is given as:
$I=\frac{P^{\prime}}{4 \pi d^{2}}$
$=\frac{5}{4 \pi(1)^{2}}=0.398 \mathrm{~W} / \mathrm{m}^{2}$
(b) Distance of a point from the bulb, d1 = 10 m
Hence, intensity of radiation at that point is given as:
$I=\frac{P^{\prime}}{4 \pi\left(d_{1}\right)^{2}}$
$=\frac{5}{4 \pi(10)^{2}}=0.00398 \mathrm{~W} / \mathrm{m}^{2}$