In YDSE shown in figure a parallel beam of light is incident on the slits from a medium of refractive index `n_(1)`. The wavelength of light in this medium is `lambda_(1)`. A transparent of thickness t and refractive index `n_(3)` is put in front of one slit. The medium between the screen and the plane of the slits is `n_(2)`. The phase difference between the light waves reaching point O (symmetrical, relative to the slits) is

Options

A. `(2 pi)/(n_(1) lambda_(1)) (n_(3) - n_(2)) t`
B. `(2 pi)/(lambda_(1)) (n_(3) - n_(2)) t`
C. `(2 pi n_(1))/(n_(2) lambda_(1)) ((n_(3))/(n_(2)) - 1) t`
D. `(2 pi n_(1))/(lambda_(1)) (n_(3) - n_(2))t`

Answer

a

Explanation

Optical path difference the waves `= (n_(3) - n_(2)) t`
`:.` Phase difference `= 2 pi ((n_(3) - n_(2))t)/(lambda_("vacuum")) = 2 pi ((n_(3) - n_(2))t)/(n_(1) lambda_(1))`