Q: In Young’s double slit experiment, using monochromatic light, fringe pattern shifts by a certain distance on the screen when a mica sheet of refractive index 1.6 and thickness 1.964 μm is introduced in the path of one of the two waves.Now mica sheet is removed and distance between slit and screen is doubled, distance between successive maxima or minima remains unchanged. The wavelength of the monochromatic light used in the experiment is

(a) 4000 Å

(b) 5500 Å

(c) 5892 Å

(d) 6071 Å

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^{-6}m

Additional path diff. introduced on account of mica sheet

=(µ-1)t = x d/D

When distance between the slit and screen is doubled, then fringe width

β =(2λ D)/d

As β = x

$ \displaystyle \frac{2 \lambda D}{d} = \frac{(\mu -1)t D}{d} $

$ \displaystyle \lambda = \frac{(\mu – 1) t}{2} $

$\displaystyle \lambda = \frac{(1.6 – 1) 1.964 \times 10^{-6}}{2} $

λ = 5892 × 10^{-10} m

λ = 5892 A °