Question

Eye at the lowest radiated power of 1,2 x10 x (- 17) W. Determine how many photons of light with a wavelength of 500nm fall on the retina of the eye every second

Answer 1

Answer:

$\frac{n}{t} = 30\ photons/s$

Explanation:

The radiated power can be given in terms of the wavelength as follows:

$Rasiated\ Power = \frac{nE}{t} = \frac{nhc}{\lambda t}$

where,

Radiated Power = 1.2 x 10⁻¹⁷ W

n = no. of photons = ?

h = plank's constant = 6.625 x 10⁻³⁴ J.s

c = speed of light = 3 x 10⁸ m/s

λ = wavelength = 500 nm = 5 x 10⁻⁷ m

t = time

Therefore,

$1.2\ x\ 10^{-17}\ W = \frac{n(6.625\ x\ 10^{-34}\ J.s)(3\ x\ 10^8\ m/s)}{(5\ x\ 10^{-7}\ m)(t) }\\\\\frac{n}{t} = \frac{1.2\ x\ 10^{-17}\ W}{3.975\ x\ 10^{-19}\ J}\\\\\frac{n}{t} = 30\ photons/s$