Physics help: Diffraction grating, Interference?

Updated on August 6, 2022

If the planes of a crystal are 3.50 (1 A= 10^-10m = Ångstrom unit) apart, what wavelength of electromagnetic waves are needed so that the first strong interference maximum in the Bragg reflection occurs when the waves strike the planes at an angle of 15.0 degrees?

I actually did get the answer of .181 nm, but I don’t understand why this is correct.

What I initially tried was dsin(theta)=m(lambda), where d= distance between slits, theta is the angle, m is just a coefficient and since it wants the first interference maximum, its just 1 in this case, and lambda is the wavelength. Using this, i got an answer half of the correct answer.

What does the spacing between the planes of the crystal mean? I took it as the width of the slit, which really isn’t d for the equation above, but I didn’t know what else to use. The picture I drew to represent this basically had a bunch of lines seperated by 3.5*10^-10, but I didn’t know what to do with this. Anyway, when I tried d=2*3.5*10^-10 instead of just 3.5*10^-10, I got the correct answer.

I’m not sure if this is purely coincidence as I don’t understand why what I did works. If anyone has a good explanation and run me through your thought process I’d really appreciate. Thanks.

• You need to look up the “Bragg equation” where

2 d sinø = m (lambda)

The (2) is there because this is reflection interference from flat sheets of atoms which are layered on top of each other ( like pages of a book ) so the is a path difference (d sin ø) between the incident rays plus the same path difference again between the reflected rays.

Its easy once you look at the diagrams.

Source(s): Old teacher and “Essentials of Physics” Whelan and Hodgson , which I had to look up because I knew there was something different about reflection interference but I couldn’t recall the detail.
• the grating equation is: d*sin(?) = m? the place d is the spacing, ? is the attitude m is the order and ? is the wavelength. all of us comprehend: d*sin(26) = m(420nm) d*sin(28) = m? divide those 2, the unknows d and m vanish, and we get: sin(26)/sin(28) = 420nm/? ? = 420nm*sin(28)/sin(26) ? = 449.79nm

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