diffraction grating

2010-03-24 9:43 am

When yellow sodium light, wavelength = 589nm falls on a diffraction grating, its first-order peak on a screen 60.0 cm away falls 3.32 cm from the central peak. Another source produces a line 3.71 cm from the central peak. What is the wavelength of the new source? How many lines/cm are on the grating?

回答 (1)

天同

2010-03-24 5:20 pm

✔ 最佳答案

Using the diffraction grating formula: a.sin(theta) = m.w
where a is the slit separation in the grating
[theta] is the angle of diffraction
w is the wavelength of light used
m is n integer

For first order diffraction, m=1
hence, for the sodium light: a.(3.32/60) = 589
i.e. a = 589 x (60/3,32) nm = 1.06 x 10^4 nm = 1.06 x 10^-3 cm
Therefore, lines/cm in the grating = 1/(1.06x10^-3) cm^-1 = 939 cm^-1

For the new source,
new wavelength = (1.06 x 10^4) x (3.71/60) nm = 655 nm

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