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?

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wagonbelleville wagonbelleville · Answer 1 · 2019-10-19T11:17:05+02:00

Answer

given,

the volume of eye

[tex]V = \dfrac{4}{3}\pi r^3[/tex]

[tex]V = \dfrac{4}{3}\pi 1.5^3\times 10^{-6}[/tex]

[tex]V =4.5 \times 10^{-6}[/tex]

temperature 37 = 273 + 37 = 310 K

Radiation energy density

[tex]u = aT^4[/tex]

[tex]u = \dfrac{4\sigma }{cT^4}[/tex]

energy of the BB photons

[tex]E = \dfrac{\sigma }{cT^4V}[/tex]

[tex]E = 9.9 \times 10^{-11}\ J[/tex]

Flux from the lamp

[tex]F = \dfrac{100}{4\pi \times \pi \times (0.1 \times 10^{-2})^2}[/tex]

[tex]F = 2.5 \times 10^{-5} J/s[/tex]

Full energy of lamp

[tex]N = \dfrac{F\times 2 R_{eye}}{c}[/tex]

[tex]N = \dfrac{2.5 \times 10^{-5}\times 0.03}{3\times 10^{10}}[/tex]

[tex]N = 2.5 \times 10^{-15} J[/tex]

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