- #1

James Marquez

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1. Homework Statement

1. Homework Statement

In Chapter 2, it derives the Bragg law using the diffraction condition and equation for spacing between parallel lattice planes. The Bragg law is given by:

$$2d\sin{\theta}=n\lambda$$

## Homework Equations

The Diffraction Condition:

$$2\textbf{k}\bullet\textbf{G}=G^2$$

Spacing Between Parallel Lattice Planes:

$$d=\frac{2\pi}{G}$$

Wave Vector:

$$\textbf{k}=\frac{2\pi}{\lambda}\hat{\textbf{k}}$$

## The Attempt at a Solution

I just don't see how we get the Bragg law using these two equations? I rearranged it so that

$$G=\frac{2\pi}{d}$$

But given by the diffraction condition, I see that:

$$G=2\frac{2\pi}{\lambda}\cos{\theta}$$

$$\frac{1}{d}=\frac{2\cos{\theta}}{\lambda}$$

I don't understand how the textbook arrives at that conclusion. Thank you.