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:

Options

A. `N = P lamda d^2 t//hc l^2`
B. `N = 4Plamdad^2 t // hcl^2`
C. `N = P lamda d^2 t// 4hc l^2`
D. `N = P lamda d^2 t// 16hc l^2`

Answer

A

Explanation

`E = (hc)/(lamda)`
Number of photons emitted is
`(pt)/((hc)/(lamda)) = n_0 rArr n_0 (P lamda t)/(hc)`
since the radiation is sphericall symmetric , so total number of photons entring the sensor is `n_0` times the ratio of aperture area to the area of a sphere of radius l .
`N = n_0 (pi (2d)^2)/(4pil^2) = (P lamda t)/(hc) (d^2)/(l^2)`