Question

Two flat mirrors form an angle close to 180 as shown in the figure.a source of light s is placed at equal distances b from the mirrors .A screen is at a distance a from mirrors.wavelength of light is lambda and there is a shield C that block light passing directly to the screen then

Why is sin Alpha=d/2/2b

Answer 1

Light emerging from point S gets reflected from mirrors M1​ and M2​, to interfere constructively at point O. 

This means that path difference between light travelling SM1​O and SM2​O must be λ. 

As shown in the figure,

path  SM1​O=2<(D/2​)^2+(d/2​)^2>^1/2

path  SM2​O=2<(D/2​)^2+d^2>^1/2

2<(D/2​)^2+d^2>^1/2− 2<(D/2​)^2+(d/2​)^2>^1/2​=λ

Thus using Bionomial expansion,

λ comes out to be 3d^2/2D

you can solve further on for your answer