Suppose that you have a reflection diffraction grating with n = 120 lines per mi

Question

Suppose that you have a reflection diffraction grating with n= 120 lines per millimeter. Light from a sodium lamp passes through the grating and is diffracted onto a distant screen. Two visible lines in the sodium spectrum have wavelengths 498 nm and 569 nm.

What is the angular separation ?? of the first maxima of these spectral lines generated by this diffraction grating?Express your answer in degrees to two significant figures.

How wide does this grating need to be to allow you to resolve the two lines 589.00 and 589.59 nanometers, which are a well known pair of lines for sodium, in the second order (m=2)?

Express your answer in millimeters to two significant figures.

Explanation / Answer

Distance between slit:

d=10^-3/120

=8.333*10^-6

By using:

dsin?=m?

sin?1=m?1/d

?1=arcsin(1*498*10^-9/8.33*10^-6)= 3.364

sin?2=m?2/d

?2=arcsin(1*569*10^-9/8.333*10^-6)=3.9153

Delta heta=3.9153-3.364

= 0.551

Again using:

R=589/0.55 ~= 1059.07

R = mN

m is the order

N is the number of slits

m=2

N= 1059.07/2= 529.038

width = 529.038/120 mm =4.408 mm

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