In-class problems 5 Solutions

In-class problems 5 Solutions - 1 n(6 Solve for 1 and...

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Name Student ID Section In-Class Problem, Week 8 20 May 2008 Show ALL your work, Total Points Possible = 5 1. A beam of 541 nm light is incident on a diffraction grating that has 400 grooves/mm. (a) Determine the distance between slits, d , and the angle of the second order ray. (+2pts) d = 1 400 mm - 1 = 2 . 50 × 10 - 6 m (1) (+1 pt) d sin θ = θ a = sin - 1 ± 2 × (541 × 10 - 9 m ) 2 . 50 × 10 - 6 m ! = 25 . 6 (2) (+1 pt) (b) If the entire apparatus is immersed in water, what is the new second order angle of diffraction? (+2pts) λ 2 = λ 1 n = 541 × 10 - 9 m 1 . 33 = 4 . 07 × 10 - 7 m (3) (+1 pt) d sin θ = θ b = sin - 1 ± 2 × (4 . 07 × 10 - 7 m ) 2 . 50 × 10 - 6 m ! = 19 . 0 (4) (+1 pt) (c) Show that the two diffracted rays in part (a) and (b) are related through the law of refraction. (+1pt) d sin θ a = 1 d sin θ a = 2 λ 1 (5) d sin θ b = 2 d sin θ b = 2
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Unformatted text preview: λ 1 n (6) Solve for λ 1 and equate the 2 expressions: λ 1 = d sin θ a / 2 = nd sin θ b / 2 (7) The d and 2 cancel, leaving: sin θ a = n sin θ b (8) Some possibly useful equations: Young’s double-slit: d sin θ bright = mλ ( m = 0 , ± 1 , ± 2 , ... ) d sin θ dark = ( m + 1 / 2) λ ( m = 0 , ± 1 , ± 2 , ... ) I avg = I max cos 2 ( πd sin θ λ Constructive interference in film: 2 nt = ( m + 1 / 2) λ ( m = 0 , 1 , 2 , ... ) Destructive interference in film: 2 nt = mλ ( m = 0 , 1 , 2 , ... ) Diffraction grating: d sin θ bright = mλ ( m = 1 , 2 , 3 , ... ) n 1 sin θ 1 = n 2 sin θ 2 1...
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