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 x 10¹²
• B. 2.84 x 10¹¹
• C. 9.37 x 10¹¹
• D. 6.84 x 10¹¹

Answer 1

Answer: (B)

The intensity of light at the location of your eye is
$\text{I}=\frac{\text{P}}{4\pi {\text{r}}^2}=\frac{60}{4\pi \times 4^2}W{\text{m}}^{-2}$
The energy entering into your eye per second is
${\text{P}}_1=\text{I}\times \frac{\pi {\text{d}}^2}{4}$
where d is the diameter of pupil
${\left(\text{P}\right)}_1=\frac{60}{4\pi \times 4^2}\times \frac{\pi \times {\left(2\times 10^{-3}\right)}^2}{4}$
$=\text{9.375}\times 10^{-7}J{s}^{-1}$
Let n be the number of photons entering into the eye per second, then
${\text{P}}_1=\text{n}\times \frac{\text{hc}}{\lambda }$
$\text{9.375}\times 10^{-7}=\text{n}\times \frac{1240\times \text{1.6}\times 10^{-19}}{600}$
$\text{n}=\text{2.84}\times 10^{12}photon{\text{s}}^{-1}$
So, the number of photons entering the eye in 0.1 s = 0.1 n = 2.84 x 10¹¹