Question

A ray of light is incident on a thick slab of glass of thickness $t$ as shown in the 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

• A. $t\left(1-\frac{i}{r}\right)$
• B. $rt\left(1-\frac{i}{r}\right)$
• C. $it\left(1-\frac{r}{i}\right)$
• D. $t\left(1-\frac{r}{i}\right)$

Answer 1

Answer: (C)

Lateral shift, $d = \frac{t}{cos\,r} sin(i-r)$
For small angles
$sin(i - r) \approx i - r; cos\,r \approx 1$
$d = t(i-r)$,
$ d = it[1- \frac{r}{i}]$