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# s38 - P38.4 For destructive interference si = m n and a = a...

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P38.4 For destructive interference, 5.00 cm sin 0139 36.0 cm m a a λ λ θ = = = = . and 7.98 θ = ° tan d L θ = gives ( ) tan 6.50 m tan7.98 0.912 m d L θ = = ° = 91.2 cm d = . *P38.7 The rectangular patch on the wall is wider than it is tall. The aperture will be taller than it is wide. For horizontal spreading we have width width width width 9 5 width 0.110 m 2 tan 0.0122 4.5 m sin 1 632.8 10 m 5.18 10 m 0.0122 y L a a θ θ λ = = = = × = = × For vertical spreading, similarly height 9 4 height 0.006 m 2 tan 0.000667 4.5 m 1 632.8 10 m 9.49 10 m sin 0.000667 h a θ λ θ = = × = = = × P38.12 min 1.22 y L D λ θ = = ( ) ( ) ( ) 7 3 1.22 5.00 10 0.0300 2.61 m 7.00 10 y μ × = × = y = radius of star-image L = length of eye λ = 500 nm D = pupil diameter θ = half angle P38.17 By Rayleigh’s criterion, two dots separated center-to-center by 2.00 mm would overlap when min 1.22 d L D λ θ = = . Thus, ( )( ) ( ) 3 3 9 2.00 10 m 4.00 10 m 13.1 m 1.22 1.22 500 10 m dD L λ × × = = = × . P38.27 (a) 4 6 1 2.732 10 cm 2.732 10 m 2732 nm 3660 linescm d = = × = × = sin d m θ λ = : At 10.09 θ = ° 478.7 nm λ = At , 13.71 θ = ° 647.6 nm λ =

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At , 14.77 θ = ° 696.6 nm λ = (b) 1 sin d λ θ = and so 2 2 sin d λ = θ 2 1 1 2 2 sin 2 n sin d λ λ θ θ λ
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