Question

Find the apparent depth of the object seen from just above the surface $AB$.

• A. $46\text{cm}$
• B. $36\text{cm}$
• C. $26\text{cm}$
• D. $16\text{cm}$

Answer 1

The correct option is B $36\text{cm}$

For the observer just above the surface $AB$, only two layers of medium will be counted for apparent depth.
$t_1=15\text{cm},{\mu }_2=1.5$
$t_2=20\text{cm},{\mu }_3=2$
$\Rightarrow d_{app}=\frac{t_1}{{}_1{\mu }_2}+\frac{t_2}{{}_1{\mu }_3}$
or $d_{app}=\frac{15}{\left(\frac{1.5}{1.8}\right)}+\frac{20}{\left(\frac{2}{1.8}\right)}$ .........$\left(i\right)$
Here, we will take the refractive index of both the medium with respect to the refractive index of the medium in which observer is present $({\mu }_1=1.8)$.
$i.e.$ ${}_1{\mu }_2=\frac{{\mu }_2}{{\mu }_1}=\frac{1.5}{1.8}$
${}_1{\mu }_3=\frac{{\mu }_3}{{\mu }_1}=\frac{2}{1.8}$
From eq. $\left(i\right)$,
$d_{app}=18+18=36\text{cm}$

Why this question? Caution: If observer is not in air $({\mu }_a=1),$ then be cautious and use relative refractive index of the medium.