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sp03opth

# sp03opth - PHY6938 Proﬁcieny Exam Spring 2003 Optics and...

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Unformatted text preview: PHY6938 Proﬁcieny Exam Spring 2003 March 28, 2003 Optics and Thermodynamics 1. Light of wavelength 300 nm strikes a metal plate, producing photoelectrons that move with speed of 0.002c. (a) What is the work function of the metal ? (b) What is the critical wavelength for this metal, so that photoelectrons are produced ? (c) What is the signiﬁcance of the critical wavelength ? 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 is a diverging lens of focal length −15 cm. What is the position of the ﬁnal image? Is the image real or virtual? Erect or inverted? What is the overall magniﬁcation of the image? 3. Consider a system consisting of N noninteracting spins S = 1/2 in a magnetic ﬁeld H . The Helmholtz free energy due to the Zeeman splitting gµB H is given by F = −N kT ln[2 cosh(gµB H/2kT )] , where k is the Boltzmann constant and T is the temperature. (a) Obtain the magnetization using M = −∂F/∂H . (b) What is the maximum magnetization? (c) For gµB H k T obtain the susceptibility deﬁned as χ = M/H . kT . (d) Obtain the entropy using S = −(∂F/∂T )H . (e) Discuss the entropy in the limits H = 0 and gµB H (f) Obtain the speciﬁc heat and sketch C/N k as a function of gµB H/kT . ...
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