Question

A narrow paraxial beam of light is converging towards a point I on a screen. A plane parallel plate of glass of thickness t, and refractive index $\mu$ is introduced in the path of the beam. The convergence point is shifted by

• A. $t\left(\right(1-1/\mu )$ away
• B. $t\left(\right(1+1/\mu )$ away
• C. $t\left(\right(1-1/\mu )$ nearer
• D. $t\left(\right(1+1/\mu )$ nearer

Answer 1

The correct option is A $t\left(\right(1-1/\mu )$ away

$\sin i=\frac{NP}{OP};\sin r=\frac{NP}{IP}$

${\eta }_1\sin i={\eta }_2\sin r$

${\eta }_1=n_1{n}_2=1$

$n\sin i=\sin r$

$n\frac{NP}{OP}=\frac{NP}{IP}$

$\Rightarrow \eta =\frac{NP}{IP}\times \frac{OP}{NP}=\frac{OP}{IP}=\frac{ON}{IN}$

$\eta =\frac{realdepth}{apparentdepth}$

Normal shift $=ON-\frac{ON}{\eta }=t(1-\frac{1}{\mu })$