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In YDSE shown in figure a parallel beam ...

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

A

`(2pi)/(n_(1)lambda_(1))(n_(3)-n_(2))t`

B

`(2pi)/(lambda_(1))(n_(3)-n_(2))t`

C

`(2pin_(1))/(n_(2)lambda_(1))(n_(3)/n_(2)-1)t`

D

`(2pin_(1))/(lambda_(1))(n_(3)-n_(1))t`

Text Solution

Verified by Experts

The correct Answer is:
A
Since`S_(1)O=S_(2)O`
Path diff.`(n_(3)t)/(n_(1))-(n_(2)t)/(n_(1))`
path diff.=`(n_(3)t-n_(2)t)/(n_(1))`
Path diff.`((n_(3)-n_(2))t)/(n_(1)`
path diff.=`(2pixx"Path diff")/(lambda_(1)) rArr "Path diff".=(2pi(n_(3)-n_(2))t)/(n_(1)lambda_(1))`
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