Question

An object is seen through a glass slab of thickness $36\text{cm}$ and refractive index $1.5$. The observer and the slab are dipped in water of refractive index $\mu =\frac{4}{3}$. The shift produced in the position of the object is

• A. $12\text{cm}$
• B. $4\text{cm}$
• C. $6\text{cm}$
• D. $8\text{cm}$

Answer 1

The correct option is B $4\text{cm}$

Given,
Thickness of glass slab, $t=36\text{cm}$
Refractive index of glass slab, ${\mu }_g=1.5=\frac{3}{2}$
Refractive index of water, ${\mu }_w=\frac{4}{3}$


We know that, normal shift $\left(\Delta \right)$ due to slab,
$\Delta =t(1-\frac{{\mu }_1}{{\mu }_2})$
$\Rightarrow \Delta =t(1-\frac{{\mu }_w}{{\mu }_g})$
$\Rightarrow \Delta =36(1-\frac{\frac{4}{3}}{\frac{3}{2}})$
$\therefore \Delta =4\text{cm}$

Why this question ? This question extends your conceptual understanding of lateral shift in glass slabs when the slab is placed in a medium other than air.