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Question

A double-slit apparatus is immersed in a liquid of refractive index 1.33. It has a slit separation of 1mm and distance between the plane of slits and screen 1.33m. The slits are illuminated by a parallel beam of light whose wavelength in air is 800nm
(i) Calculate the fringe width
(ii) One of the slits of the apparatus is covered by a thin glass sheet of refractive index 1.53. Find the smallest thickness of the sheet to bring the adjacent minima on the axis.

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Solution

(a) β=λDd

β=6300×1.33×10101.33×1×103

=6.3×104m

(b) Path diff. Δx

Δx=(aμzaμ21)t

Δx=0.15t

Max. at o on axis should be shifted to bring adjacent minima __.

Δx=λ22 or 0.15t=λa2μ

0.15t=6300×10102×1.33

t=1.575×106m


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