Crystal diameter and beam divergence are which kind of related?

Crystal diameter and beam divergence are which kind of related?

• A. Inversely
• B. Directly
• C. Unrelated
• D. Linearly proportional

Answer: (A)

The key idea is that diffraction from a finite crystal behaves like a limited aperture. The angular spread (divergence) of the diffracted beam is set by the size of the crystal: a larger diameter acts as a bigger aperture, which narrows the range of angles that diffract into the beam. Conversely, a smaller crystal presents a smaller aperture and produces a broader angular spread. In simple terms, you get less divergence when the crystal is bigger, and more divergence when the crystal is smaller, which means the relationship is inverse. Doubling the diameter roughly halves the divergence in the typical small-angle, diffraction-dominated regime. The other options would imply either a direct or no relationship, which contradicts the way wave diffraction from finite apertures works.

The key idea is that diffraction from a finite crystal behaves like a limited aperture. The angular spread (divergence) of the diffracted beam is set by the size of the crystal: a larger diameter acts as a bigger aperture, which narrows the range of angles that diffract into the beam. Conversely, a smaller crystal presents a smaller aperture and produces a broader angular spread. In simple terms, you get less divergence when the crystal is bigger, and more divergence when the crystal is smaller, which means the relationship is inverse. Doubling the diameter roughly halves the divergence in the typical small-angle, diffraction-dominated regime. The other options would imply either a direct or no relationship, which contradicts the way wave diffraction from finite apertures works.