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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 = 6.2610-34 Js is Planck's constant, and kB = 1.38110-23 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 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 transcendental equation 5 - x = 5e-x 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 Stefan-Boltzmann constant = 5.67 10-8 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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