Two mirrors M₁ and M₂ make an angle φ with line AB. A point source S is kept at a distance r from the point of intersection of the mirrors. A small hemispherical annular mask is kept close to S so that no ray emitted by S reaches the screen directly. The screen is at a distance b from the source. Interference of the rays reflected from M₁ and M₂ is observed on the screen. If λ is the wavelength of light, find the fringe width.

Question

G1 Physics · Accepted Answer

Use the image method. The two reflected rays behave as if they come from two virtual coherent sources S₁ and S₂ formed by reflection in mirrors M₁ and M₂. The separation between these two virtual sources is d = 2r sin 2φ. The effective distance of the screen from the virtual-source plane is D = b + 2r sin²φ. Hence the fringe width is β = λD/d = λ(b + 2r sin²φ) / (2r sin 2φ). Therefore the correct answer is A.