You are hired to design an infra-red camera that will detectintruders in the dar

Question

You are hired to design an infra-red camera that will detectintruders in the dark. Assuming that the human body is blackbody at37C (310K): A. what a wavelength should your camera be able todetect? B. how much power per squer meter does the human bodyradiate? C. how many photones per second are emitted per squer meter (assume that all photones are emitted at the wavelength found inpart A)? You are hired to design an infra-red camera that will detectintruders in the dark. Assuming that the human body is blackbody at37C (310K): A. what a wavelength should your camera be able todetect? B. how much power per squer meter does the human bodyradiate? C. how many photones per second are emitted per squer meter (assume that all photones are emitted at the wavelength found inpart A)?

Explanation / Answer

Temperature T = 310 K (A). wavelength = b / T where b= Wien's displacementconstant = 2.897×103 m·K plug the values weget   = 9.345 * 10 ^ -6m (B).power per squer meter does the human body radiate P = T ^ 4 here we assume human body is perfect blackbody So, P = ( 5.67*10^ -8 ) ( 310 ) ^ 4            =523.63 W (c). energy E = nhc / here E = P = 523.63 J          =9.345*10^ -6 m plug the values we get No.of photons per squaremeter n = E / hc where h = planck's constant = 6.625 * 10 ^ -34 Js            c= speed of light = 3 * 10 ^ 8 m / s plug the values weget   = 9.345 * 10 ^ -6m (B).power per squer meter does the human body radiate P = T ^ 4 here we assume human body is perfect blackbody So, P = ( 5.67*10^ -8 ) ( 310 ) ^ 4            =523.63 W (c). energy E = nhc / here E = P = 523.63 J          =9.345*10^ -6 m plug the values we get No.of photons per squaremeter n = E / hc where h = planck's constant = 6.625 * 10 ^ -34 Js            c= speed of light = 3 * 10 ^ 8 m / s

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