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
$I=\frac{P}{4\pi r^2}=\frac{60}{4\pi \times 4^2}W{m}^{-2}$
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
$P_1=\frac{60}{4\pi \times 4^2}\times \frac{\pi \times {\left(2\times 10^{-3}\right)}^2}{4}$
$=9.375\times 10^{-7}J{s}^{-1}$
Let $n$ be the number of photons entering into the eye per second, then
$P_1=n\times \frac{hc}{\lambda }$
$9.375\times 10^{-7}=n\times \frac{1240\times 1.6\times 10^{-19}}{600}$
$n=2.84\times 10^{12}photon{s}^{-1}$
So, the number of photons entering the eye in $0.1s$ $=0.1n=2.84\times 10^{11}$