# HW1B - Assignment 1B Physics U603 Summer 1 2006 Due...

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Assignment 1B Physics U603 Summer 1 2006 Due Tuesday, May 16 1. The addition ψ = Ae i ( k 1 x ω 1 t ) + Ae i ( k 2 x ω 2 t ) of two waves with di f erent angular frequencies ω 1 and ω 2 produces beats. Assume nearby fre- quencies, so that ω 1 = ω ω , ω 2 = ω + ω , k 1 = k k ,and k 2 = k + k , and show that the real part of the wave function is 2 A cos ( kx ωt )cos( ) .S k e t c h Re ψ as a function of posi- tion for the case where ω =5 ω and explain the signi f cance of the quantities ω/k and ω/ k (known as the phase speed and the group speed, respectively). 2. A 1.3 mW HeNe laser produces a Gaussian beam of wavelength λ =633 nm and a 0.24 mm diameter at the beam waist. (a) Determine the angular divergence of the beam, the Rayleigh range, and the beam diameter at the surface of the Moon. (b) Compare the optical intensity at the beam waist with the intensity 14 cm from a 100 W point source.

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## This note was uploaded on 08/26/2008 for the course PHYSICS 603 taught by Professor Sage during the Summer '06 term at Northwestern.

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HW1B - Assignment 1B Physics U603 Summer 1 2006 Due...

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