Question

A sensor is exposed for time t to a lamp of power P placed at a distance l. The sensor has an opening that is 4d in diameter. Assuming all energy of the lamp is given off as light, the number of photons entering the sensor if the wavelength of light is $\lambda$ is

• A. $N=P\lambda d^{2}t/hc{l}^2$
• B. $N=4P\lambda d^{2}t/hc{l}^2$
• C. $N=P\lambda d^{2}t/4hc{l}^2$
• D. $N=P\lambda d^{2}t/16hc{l}^2$

Answer 1

The correct option is A $N=P\lambda d^{2}t/hc{l}^2$

Power is given by:

$P=\frac{E}{t}=\frac{nhc}{\lambda t}$

$n=\frac{P\lambda t}{hc}$

where $n$ is the total number of photons emitted by the source.
The number of photons entering the sensor will be in proportion to the area of the sensor relative to the bigger sphere of radius $l$.
Thus, the number of photons entering the sensor is given by

$N=\frac{P\lambda t}{hc}\times \frac{\pi {\left(2d\right)}^2}{4\pi l^2}$

Thus, $N=\frac{P\lambda d^{2}t}{hc{l}^2}$