Question

A $60W$ bulb is placed at a distance of $4m$ from you. The bulb is emitting light of wavelength $600nm$ uniformly in all directions. In $0.1s$ , how many photons will enter your eye, if the pupil of the eye has a diameter of $2mm$ ? [Take $hc=1240eVnm$ ]

• A. $2.84\times 10^{12}$
• B. $2.84\times 10^{11}$
• C. $9.37\times 10^{11}$
• D. $6.84\times 10^{11}$

Answer 1

Answer: (B)

The intensity of light at the location of your eye is
$I=\frac{P}{4 \pi r^{2}}=\frac{60}{4 \pi \times 4^{2}}Wm^{- 2}$
The energy entering into your eye per second is
$P_{1}=I\times \frac{\pi d^{2}}{4}$
where $d$ is the diameter of the pupil
$P_{1}=\frac{6 0}{4 \pi \times 4^{2}}\times \frac{\pi \times \left(2 \times 1 0^{- 3}\right)^{2}}{4}$
$=9.375\times 10^{- 7}Js^{- 1}$
Let $n$ be the number of photons entering into the eye per second, then
$P_{1}=n\times \frac{h c}{\lambda }$
$9.375\times 10^{- 7}=n\times \frac{1 2 4 0 \times 1 .6 \times 1 0^{- 1 9}}{6 0 0}$
$n=2.84\times 10^{12}photons^{- 1}$
So, the number of photons entering the eye in $0.1s$ $=0.1n=2.84\times 10^{11}$