A ray of light falls at an angle of `30^(@)` onto a plane-parallel glass plate and leaves it parallel to the initial ray. The refractive index of the glass is `1.5`. What is the thickness of `d` of the plane if the distances between the rays is `3.82cm` ? [Given: `sin^(-1) ((1)/(3)) = 19.5^(@), cos 19.5^(@) = 0.94, sin 10.5^(@) = 0.18`]

Explanation

Using `s = (d sin (i-r))/(cost r)`
`rArr d = (3.82xx cos r)/(sin (30^(@) - r))..........(1)`
Also, `1.5 = (sin 30^(@))/(sin r) rArr sin r = (1)/(3)`
So, `r = 19.5^(@)`
So, `d = (3.82xxcos 19.5^(@))/(sin(30^(@) - 19.5^(@)) ) = (3.82xx0.94)/(sin 10.5^(@)) = (3.82xx0.94)/(0.18) = 19.948cm`
`= 0.2m`