A rays of light is incident on a thick slab of glass of thickness t as shown in figure. The emergent ray is parallel to the incident ray but displaced sideways by a distance d. If the angles are small then d is

Options

A. `t(1+(i)/(r))`
B. `rt(1-(i)/(r))`
C. `it(1-(r)/(i))`
D. `t(1+(r)/(i))`

Answer

C

Explanation

Lateral shift, ` d = (t)/(cosr) sin (i-r)`
For small angles `sin(i-r) ~~ i - r`, `cosr~~1`
`d = t(i-r), d =` it `[1- (r)/(i)]`