In the Young's double slit experiment, the distance between the slits varies in time as d t = d 0 + a 0 sin ω t ; where d 0 , ω and a 0 are constants. The difference between the largest fringe width and the smallest fringe width obtained over time is given as:

Step-by-step solution

Fringe width, β = λ D d β max ⇒ d min and β min ⇒ d max d = d 0 + a 0 sin ω t d max = d 0 + a 0 and d min = d 0 - a 0 ∴   β min = λ D d 0 + a 0 and ∴   β max = λ D d 0 - a 0 β max - β min = λ D d 0 - a 0 - λ D d 0 + a 0 = 2 λ D a 0   d 0 2 - a 0 2