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Unformatted text preview: PHY6938 Proficieny 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 () = 2hc2 1 , 5 exp(hc/k T )  1 B where is the wavelength, c = 3.00 108 m/s is the speed of light, h = 6.261034 Js is Planck's constant, and kB = 1.3811023 J/K is Boltzmann's constant. (a) Make a sketch of F () as a function of . (b) The power density F () has a maximum at a particular wavelength, max . Derive the relation T max 2.90 103 Km. This result is known as Wien's Displacement law. Hint: It may be useful to note that the two roots of the transcendental equation 5  x = 5ex are 0 and approximately 4.965. (c) Show that the total power radiated per unit area is given by the StefanBoltzmann law, P = T 4 , with the StefanBoltzmann constant = 5.67 108 mW 4 . 2K Hint: The following integral may be useful:
inf  inf 4 x3 dx = ex  1 15 2. Two lenses are separated by 35 cm. An object is placed 20 cm to the left of the first lens, which is a converging lens of focal length 10 cm. The second lens if a diverging lens of focal length 15 cm. What is the position of the final image ? Is the image real or virtual ? Erect of inverted ? What is the overall magnification of the image? ...
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 Fall '1
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 Thermodynamics, Power, Radiation

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