Question

Evaluate the energy of the blackbody photons inside your eye. Compare this with the visible energy inside your eye while looking at a 100-W light bulb that is 1 m away. You can assume that the light bulb is 100% efficient, although in reality it converts only a few percent of its 100 watts into visible photons. Take your eye to be a hollow sphere of radius 1.5 cm at a temperature of 37◦C. The area of the eye’s pupil is about 0.1 cm2. Why is it dark when you close your eyes?

Answer 1

given,

the volume of eye

`V = (4)/(3)\pi r^3`

`V = (4)/(3)\pi 1.5^3* 10^(-6)`

`V =4.5 * 10^(-6)`

temperature 37 = 273 + 37 = 310 K

Radiation energy density

`u = aT^4`

`u = (4\sigma )/(cT^4)`

energy of the BB photons

`E = (\sigma )/(cT^4V)`

`E = 9.9 * 10^(-11)\ J`

Flux from the lamp

`F = (100)/(4\pi * \pi * (0.1 * 10^(-2))^2)`

`F = 2.5 * 10^(-5) J/s`

Full energy of lamp

`N = (F* 2 R_(eye))/(c)`

`N = (2.5 * 10^(-5)* 0.03)/(3* 10^(10))`

`N = 2.5 * 10^(-15) J`

when we close your eyes the light from the source stop and the black body photon starts hitting retina which will cause darkness.