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

Answer

given,

the volume of eye

$V = \dfrac{4}{3}\pi r^3$

$V = \dfrac{4}{3}\pi 1.5^3\times 10^{-6}$

$V =4.5 \times 10^{-6}$

temperature 37 = 273 + 37 = 310 K

Radiation energy density

$u = aT^4$

$u = \dfrac{4\sigma }{cT^4}$

energy of the BB photons

$E = \dfrac{\sigma }{cT^4V}$

$E = 9.9 \times 10^{-11}\ J$

Flux from the lamp

$F = \dfrac{100}{4\pi \times \pi \times (0.1 \times 10^{-2})^2}$

$F = 2.5 \times 10^{-5} J/s$

Full energy of lamp

$N = \dfrac{F\times 2 R_{eye}}{c}$

$N = \dfrac{2.5 \times 10^{-5}\times 0.03}{3\times 10^{10}}$

$N = 2.5 \times 10^{-15} J$

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