A light ray is incident at an angle of `45^@` with the normal to a `sqrt2` cm thick plate` (mu=2.0)`. Find the shift in the path of the light as it emerges out from the plate.

Explanation

Consider the ray diagram as shown below

Lateral shift, BC`=(tsin(i-r))/(cosr)=tsini[1-(cosi)/(sqrt(mu_(2)-sin^(2)i))]`
`=4sin45^(@)[1-(cos45^(@))/(sqrt((2)^(2)-(sin^(2)45^(@))))]`
`=4/sqrt2[(1//sqrt2)/(sqrt(4-1//2))]=2sqrt2(1/sqrt7)=1.06 cm`