A double slit apparatus is immersed in a liquid of refractive index 1.33. It has slit and the screen 1 mm. The slits are illuminated by a parallel beam of light whose wavelength in air is `6300 Å`
a. calculate the fringe width.
b. 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 athe adjacent minima on the axis.

Options

A. `2.132mu m`
B. `2.512mu m`
C. `6.521mu m`
D. `1.579mu m`

Answer

D

Explanation

Let t be the thickness of the glass slab. Path difference due to glass slab at center O.
`Delta x = ((mu_("glass"))/(mu_("liquid"))- 1)t = ((1.53)/(1.33) - 1)t`
or `Delta x = 0.15 t`

Now, for the intensity to be minimum at O, this path difference should be equal to `(lambda')/(2)`
`Delta x = (lambda')/(2) or 0.15 t = (4737)/(2) Å`
`t = 15790 Å or t = 1.579 mm`