A ray of light is incident on the surface of a glass plate of thickness `t`. If the 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. `tthetan//(n+1)`
B. `ttheta(n-1)//n`
C. `tthetan//(n-1)`
D. `ttheta//(n+1)//n`

Answer

B

Explanation

Lateral shift `y=(tsin(i-r))/(cosr)=tsini-tcosi(sinr)/(cosr)`
`(1xxsini=nsinr)`
`=tsini-tcost(sini//n)/(sqrt(1-(sin^2i)/(n^2)))=tsini[1-(cosi)/(sqrt(n^2-sin^2i))]`
When i is small, `sin^2 i` is negligible, `cos i=1`, `sin i=sin theta=theta`
`=ttheta(1-1/n)=(ttheta(n-1))/(n)`