Using monochromatic light of wavelength λ, an experimental sets up the Young's double slit experiment in three ways as shown. If she observes that y=β', the wavelength of light used is : 540nm 560nm 580nm 520nm

The fringe width in Young's double slit experiment is given by λD/d
When the slab of refractive index μ is placed in front of one of the slits, the new path difference at any point P on screen is
S2P − (S1P + μt − t) = S2P − S1P − (μ − 1)t = yD/d − (μ − 1)t
For central bright fringe the path difference should be zero
⇒ yD/d − (μ − 1)t = 0
central bright fringe will now occur at y = (μ − 1)tD/d
the fringe patterns shifts by D(1 − μ)t/d
The second maxima will be at 2D(1 − μ)t/d
fringe width = difference between position of two consecutive maximas
w' = 2D(1 − μ)t/d − D(1 − μ)t/d
The new fringe width is y = D(1 − μ)t/d
Now the distance between screen and source is doubled the fringe width is 2Dλ/d
The two fringe widths are equal
D(1 − μ)t/d = 2Dλ/d
substituting values λ = 540nm