phy- diffraction

2011-02-22 1:21 am

When white light (400nm - 700nm) is incident normally on a grating, the first order spectrum has an angular width of 30°, how many lines per mm are there on the grating?(Ans：1.23x10^3 per mm)

更新1:

點解好似無用到30度? (the first order spectrum has an angular width of 30°)

回答 (1)

用戶25975

2011-02-22 5:36 am

✔ 最佳答案

Let d be the spacing between successive lines on the grating, then:

For the first order:

d sin θR = 7 x 10-7

d sin θV = 4 x 10-7

So:

d(sin θR + sin θV) = 11 x 10-7

2d sin [(θR + θV)/2] cos [(θR - θV)/2] = 11 x 10-7

2d sin [(θR + θV)/2] cos 15 = 11 x 10-7 ... (1)

d(sin θR - sin θV) = 3 x 10-7

2d sin [(θR - θV)/2] cos [(θR + θV)/2] = 3 x 10-7

2d sin 15 cos [(θR + θV)/2] = 3 x 10-7 ... (2)

Using (1) to divide (2):

tan [(θR + θV)/2]/tan 15 = 11/3

tan [(θR + θV)/2] = (11 tan 15)/3 = 0.982

(θR + θV)/2 = 44.5

Sub this into either (1): 2d sin 44.5 cos 15 = 11 x 10-7d = 8.12 x 10-7 mHence in 1 mm, no. of lines is:

10-3/(8.12 x 10-7) = 1230

2011-02-21 21:57:22 補充：
θR - θV = 30 度

(θR - θV)/2 = 15 度

參考: 原創答案

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