19_Ch 24 College Physics ProblemCH24 Wave Optics

19_Ch 24 College Physics ProblemCH24 Wave Optics - Wave...

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Wave Optics 321 (b) In the second order, . The second order images for the above wavelengths will be found at angles 2 m = ( ) [ ] 1 1 2 1 2 sin 2sin d sin θ λ θ = = m This yields: for 479 n λ = , 2 20.5 θ = ° ; for 647 nm λ = , 2 28.3 θ = ° ; and for 698 nm λ = , 2 30.7 θ = ° 24.36 (a) The longest wavelength in the visible spectrum is 700 nm, and the grating spacing is 3 6 1 mm 1.67 10 mm 1.67 10 m 600 d = = × = × Thus, ( ) 6 max 9 1.67 10 m sin90.0 sin90.0 2.38 700 10 m red d m λ × ° ° = = = × so 2 complete orders will be observed. (b) From d sin λ θ = , the angular separation of the red and violet edges in the first order will be 9 9 1 1 1 1 6 6 700 10 m 400 10 m sin sin sin 1.67 10 m 1.67 10 m violet d d λ λ sin red θ × × = = × × or 10.9 θ = ° 24.37 The grating spacing is
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