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)lamda_(1))(n_(3)-n_(2))t`
B. `(2pi)/(lamda_(1))(n_(3)-n_(2))t`
C. `(2pin_(1))/(n_(2)lamda_(1))((n_(3))/(n_(2))-1)t`
D. `(2 pin_(1))/(lamda_(1))(n_(3)-n_(2))t`

Answer

A

Explanation

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