ch36-p054 - 54. We are given the number of lines per...

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54. We are given the “number of lines per millimeter” (which is a common way to express 1/ d for diffraction gratings); thus, 1 d = 160 lines/mm d = 6.25 × 10 6 m . (a) We solve Eq. 36-25 for θ with various values of m and λ. We show here the m = 2 and λ = 460 nm calculation: () 9 11 1 6 10 m) sin sin sin 0.1472 8.46 . 6.25 10 m m d λ −− ⎛⎞ 2(460× == = = ° ⎜⎟ × ⎝⎠ Similarly, we get 11.81° for m = 2 and λ = 640 nm, 12.75° for m = 3 and λ = 460 nm, and 17.89° for m = 3 and λ = 640 nm. The first indication of overlap occurs when we compute the angle for m = 4 and λ = 460 nm; the result is 17.12° which clearly shows overlap with the large-wavelength portion of the
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