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.

Answer

(i)`y=2cm`,(ii)`mu=1.0016`

Explanation

Path difference=`(SS_(1)+S_(1)B)-(SS_(2)+S_(2)B)`
`=(SS_(1)-SS_(2))-(S_(2)B-S_(1)B)`
`=dsinalpha-dsintheta`
Since B is central maxima
` =dsinalpha-dsintheta=0`
`sin alpha=sintheta`
`(40)/(200)=(x_(0))/(10)`
`x_(0)=2cm`
when liquid filled central bright is obtained at `Q`which is symmertrical form`S_(1)S_(2).`
`=(SS_(1)-SS_(2))-(S_(2)Q-S_(1)Q)`
so path difference=`dsinalpha-(mu-1)xx10`
For central bright at `Q`,path difference=`0`
`dsinalpha-(mu-1)xx10=0`
`(mu-1)xx10=dsinalpha`
`(mu-1)xx10=d tan alpha`
`(mu-1)xx10=8xx10^(-2)xx(1)/(5)`
`mu-1=1.6xx10^(-3)`
`mu=1.0016`