Question

X-rays of wavelength λ get reflected from parallel planes of atoms in a crystal with spacing d between two planes as shown in the figure. If the two reflected beams interfare constructively,Then the condition for maxima will be(n is the order of interference fringe)

• A. d tanθ=nλ
• B. d sinθ=nλ
• C. 2d cosθ=nλ
• D. 2d sinθ=nλ

Answer 1

The Correct Option is D

In the diagram provided, the path difference between the beams reflected from consecutive planes is AM+AN=2dsinθ. For constructive interference to occur, the path difference must equal an integer multiple of the wavelength, represented as 2dsinθ=nλ.

The correct option is(D): 2d sinθ=nλ

Answer 2

The condition for constructive interference (maxima) in the case of X-rays reflected from parallel planes in a crystal is given by Bragg's Law. According to Bragg's Law:
\(2 d \sin \theta = n \lambda\)

where:
d is the spacing between the planes of atoms in the crystal,
\(\theta\) is the angle of incidence (and reflection) of the X-rays with respect to the planes,
n is the order of the interference fringe (an integer),
\(\lambda\) is the wavelength of the X-rays.

So, the correct option is (D): \(2d \sin \theta = n \lambda\)