Question

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

• A. $t(1-\frac{1}{\mu })$ away
• B. $t(1+\frac{1}{\mu })$ away
• C. $t(1-\frac{1}{\mu })$ nearer
• D. $t(1+\frac{1}{\mu })$ nearer

Answer 1

The correct option is A $t(1-\frac{1}{\mu })$ away

$\begin{array}{c}\text{shift}=\text{Real depth-apparent depth}\\ \mu =\frac{\text{Real depth}}{\text{apparent depth}}\\ \Rightarrow \mu =\frac{t}{\text{apparent depth}}\\ \begin{array}{cc}\frac{t}{\mu }& =\text{Apparent depth}\\ \text{Shif}t& =t-\frac{t}{\mu }\\ =& t(1-\frac{1}{\mu })\text{away}\end{array}\end{array}$