51. (a) Since the resolving power of a grating is given by R = λ/ ∆ λ and by Nm , the range of wavelengths that can just be resolved in order m is ∆ λ = λ/Nm .He re N is the number of rulings in the grating and λ is the average wavelength. The frequency f is related to the wavelength by fλ = c ,where c is the speed of light. This means f ∆ λ + λ ∆ f =0,so ∆ λ = − λ f ∆ f = − λ 2 c ∆ f where f = c/λ is used. The negative sign means that an increase in frequency corresponds to a decrease in wavelength. We may interpret ∆ f as the range of frequencies that can be resolved and take it to be positive. Then, λ 2 c ∆ f = λ Nm and ∆ f = c Nmλ . (b) The diFerence in travel time for waves traveling along the two extreme rays is ∆ t =∆
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.