Question

A glass slab $(\mu =1.5)$ of thickness $2\text{cm}$ is placed on a spot. The shift of spot if it is viewed from top will be

• A. $\frac{2}{3}\text{cm}$
• B. $\frac{4}{3}\text{cm}$
• C. $\frac{5}{3}\text{cm}$
• D. $\frac{7}{3}\text{cm}$

Answer 1

The correct option is A $\frac{2}{3}\text{cm}$

We know that,
${\mu }_{21}=\frac{{\mu }_2}{{\mu }_1}=\frac{\text{real depth}}{\text{apparent depth}}$
where ${\mu }_1$ is the refractive index of the medium in which the observer is present and ${\mu }_2$ is the refractive index of the medium in which the object is kept.
Here, ${\mu }_1$ is the refractive index of air and ${\mu }_2$ is the refractive index of glass slab.
So, $\frac{1.5}{1}=\frac{2}{\text{apparent depth}}$
$\Rightarrow \text{apparent depth}=\frac{4}{3}\text{cm}$

Hence, shift of spot $=2-\frac{4}{3}=\frac{2}{3}\text{cm}$

Why this question? Tips: Apply the concept of real depth and apparent depth. The real depth of the spot will be the thickness of the slab because the spot is at bottom.