Wave Optics

Bragg’s Law and Path Difference Explanation:

In X-ray diffraction by a crystal, waves are reflected from different parallel crystal planes. The key idea is that the path difference between the rays reflected from successive planes should lead to constructive interference.

Geometry Insight:

Let the distance between two successive crystal planes be d. An incident ray hits the first plane at an angle θ and reflects, while another ray enters to the second plane, reflects, and emerges parallel to the first ray.

The extra distance traveled by the second ray is the sum of two segments:

• AM = distance going into the plane =
• AN = distance coming out of the plane =

Total path difference =

Condition for Constructive Interference:

To observe a strong reflected beam, the path difference should be an integer multiple of the wavelength λ, that is:

Where:

• d = spacing between planes
• θ = glancing angle
• n = order of diffraction (an integer)
• λ = wavelength of X-ray

Conclusion: The correct relation that gives the condition for constructive interference in X-ray diffraction is:

Option (D):