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Question
(a) Given a 10000 lines per centimeter diffraction grating, the wavelengths 409.9 nm, 433.7 nm, 486.3 nm, 656.1 nm, form first-order maxima at angles of $24.2^\circ$, $25.7^\circ$, $29.1^\circ$, $41.0^\circ$, respectively. What do the four angles become if a 5000-line-per-centimeter diffraction grating is used? (b) Using this grating, what would the angles be for the second- order maxima? (c) Discuss the relationship between integral reductions in lines per centimeter and the new angles of various order maxima.
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Final Answer
  1. $\theta_{\textrm{a1}}= 11.8^\circ$, $\theta_{\textrm{b1}} = 12.5 ^\circ$, $\theta_{\textrm{c1}} = 14.1^\circ$, $\theta_{\textrm{d1}} = 19.2^\circ$
  2. $\theta_{\textrm{a2}} = 24.2^\circ$, $\theta_{\textrm{b2}} = 25.7^\circ$, $\theta_{\textrm{c2}} = 29.1^\circ$, $\theta_{\textrm{d2}} = 41.0^\circ$
  3. The integral factor by which the lines per centimeter is reduced is the order of the maximum which will have the same angle as the first order maximum with the original lines per centimeter.
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OpenStax College Physics Solution, Chapter 27, Problem 27 (Problems & Exercises) (5:02)

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