The angle of the first order diffraction

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The angle of the first order diffraction (m=1) for X-rays diffracting from a crystal with a plane spacing of 0.175 nm is calculated to be 69 degrees. The second order diffraction (m=2) occurs at 45 degrees, indicating that higher order reflections correspond to larger Bragg angles. The discussion references Bragg's law, which states that mλ = 2d sin(θ). The calculations suggest that as the order increases, the angle decreases, confirming the relationship between order and angle. The conclusion supports that the calculated angle is valid since it exceeds 45 degrees.
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Homework Statement



What is the angle of the first order diffraction, m=1, when X-rays diffract from a crystal in which a spacing between atomic planes is 0,175nm? The 2nd diffraction, m=2, occurs at 45o.

Homework Equations


Δr=2dcosθm=mλ
m+1/m = cos45/cosθm , because when the m increases the θm decreases.

The Attempt at a Solution


m+1/m = cos45/cosθ1
θ1 = 69o.

What do you think? Just asking because I am not 100% sure.
 
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Last time I checked, Bragg's law was m lambda = 2 d sin(theta)...

Higher order reflections always occur at larger Bragg angles.
 
I my case it is cosθm. Yep, I think this should be the right answer because the angle is bigger than 45o.
 

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