fa02opth_sol

fa02opth_sol - PHY6938 Proficiency Exam Fall 2002 Optics...

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Unformatted text preview: PHY6938 Proficiency Exam Fall 2002 September 13, 2002 Optics and Thermodynamics 1. Objects at finite temperature T emit electromagnetic radiation with a continuous spectrum, called Blackbody radiation. The radiated power per unit area and unit wavelength is given by the function F ( λ ) = 2 πhc 2 λ 5 1 exp( hc/λk B T )- 1 , where λ is the wavelength, c = 3 . 00 × 10 8 m/s is the speed of light, h = 6 . 26 × 10- 34 Js is Planck’s constant, and k B = 1 . 381 × 10- 23 J/K is Boltzmann’s constant. (a) Make a sketch of F ( λ ) as a function of λ . F( λ29 λ (b) The power density F ( λ ) has a maximum at a particular wavelength, λ max . Derive the relation T λ max ≈ 2 . 90 × 10- 3 Km. This result is known as Wien’s Displacement law. Hint: It may be useful to note that the two roots of the transcen- dental equation 5- x = 5 e- x are 0 and approximately 4.965. To find the maximum of F ( λ ) we have to take the derivative of F ( λ ) with respect to λ . Let x = hc λkT .....
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This note was uploaded on 03/11/2012 for the course PHY 3900 taught by Professor Staff during the Fall '1 term at FSU.

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fa02opth_sol - PHY6938 Proficiency Exam Fall 2002 Optics...

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