This document discusses using Bragg's law to calculate the wavelength range passing through an analyzer device. Bragg's law relates the wavelength of electromagnetic radiation to the diffraction angle when scattered from a crystal. The document gives that for a wavelength of 0.149 nm, the first-order Bragg peak occurs at an angle of 15.15 degrees. Using Bragg's law and taking the derivative with respect to angle, the document calculates that for an angular range of the analyzer of 0.015 degrees, the corresponding wavelength range passing through is 1.439 x 10^-4 nm.

1. 1
A certain device for analyzing
electromagnetic radiation is
based on the Bragg scattering
of the radiation from a crystal.
For radiation of wavelength
0.149 nm, the first-order Bragg
peak appears centered at an
angle of 15.15◦
. The aperture of
the analyzer passes radiation
in the angular range of 0.015◦
.
What is the corresponding
range of wavelengths passing
through the analyzer?
Helping Tools
No.1
OR
No.2
No.3

2. 2
Solution
Using Bragg's Law,
2 sin --------------- (1)
for 1st order Bragg peak, 1
(1) 2 sin
differentiating w.r.t
2 cos
2 cos --------- (2)
n d
n
d
d
d
d
d d d
 
 




  
=
=
 =
=
 =

3. 3
,
2 sin
2sin
(2) 2( )cos
2sin
cot -------- (3)
Now
d d
d d
d d

 


  

   
=  =
 =
 =
9
4
4
4
Using
0.149 0.149 10
cot15.15 3.69
0.015
0.015
57.30
2.6178 10
in eq.(3), we get
0.149 3.69 2.6178 10
0.0001439 1.439 10
nm X m
d rad
X rad
d nmX X X
nm X nm



−
−
−
−
= =
=
= =
=
=
= =