A vessel ABCD of `10 cm` width has two small slits `S_(1)` and `S_(2)` sealed with idebtical glass plates of equal thickness. The distance between the slits is `0.8 mm`. POQ is the line perpendicular to the plane AB and passing through O, the middle point of `S_(1)` and `S_(2)`. A monochromatic light source is kept at `S, 40 cm` below `P` and `2 m` from the vessel, to illuminate the slits as shown in the figure. Calculate the position of the central bright fringe on the other wall CD with respect of the line `OQ`. Now, a liquid is poured into the vessel and filled up to `OQ`. The central bright fringe is fiund to be at Q. Calculate the refractive index of the liquid.

Explanation

Path diffenence before slits
`SS_(1)-SS_(2)=d sin alpha`
Path difference after slits
`S_(2)A-S_(1)A=d sintheta`
As angles are small, `sin alpha=tan alpha, sin theta=tantheta`
For `A` to be central maximum
`d sin alpha=dsintheta implies tan alpha=tantheta`
`40/200=y/10implies y=2 cm`
When vessel is filled with liquid, path difference at `Q` after slits
`=(mu-1)t=(mu-1)xx10`
At `Q`:
`d sin alpha=(mu-1)xx10`
`d tan alpha=(mu-1)xx10`
`0.8/10xx40/200=(mu-1)xx10`
`mu=1.0016`