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. `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

Lateral shift (d) `= (t sin (I - r))/(cos r ) `
Here, i = `theta `
and for small angle
`sin (theta - r ) = theta - r `
and cos r = 1
`therefore " " d = t (theta - r)`
Since, `(sin i)/(sin r) = ( sin theta)/( sin r ) = n rArr n = (theta)/(r ) rArr r = (theta)/(n )`
`d = r (theta - (theta)/(n)) rArr d = t theta (1 - (1)/(n))`