A ray of light is incident on the surface of a glass plate of thickness `t`. I fthe angle of incidence `theta` is small, the emerging ray would be displaced side ways by an amount
`[Take `n =` refractive index of glass)

Options

A. `t theta n//(n+1)`
B. `t theta(n-1)//n`
C. `t theta n//(n - 1)`
D. `t theta (n + 1)//n`

Answer

B

Explanation

In `Delta BCE`,

`sin (theta - r) = (CE)/(BC)`
`CE = BC sin (theta -r)`
or `d = BC sin (theta - r)`
IN `Delta BMC`,
`cos r = (BM)/(BC)`
or `BC = (BM)/(cos r) = (t)/(cos r)`
From Eqs. (i) and (ii), we get
`d = (t)/(cos r) sin (theta - r)`
or `d = (t)/(cos r) (sin theta cos r - cos theta sin r)`
or `d = t (sin theta - cos theta tan r)`
If `n` is the refractive index of material of slab (glass)
w.r.t air, then
`n = (sin theta)/(sin r)`
For small angle, `n = (theta)/(r )`
or `r = (theta)/(n)` and `d = t (theta - 1.r)`
`[ :' sin theta~~ theta` and `cos theta~~ 1` if `theta` is small]
`d = t (theta - (theta)/(n)) = t theta (1 - (1)/(n))`
or `d = (t theta(n - 1))/(n)`