Question

Determine the apparent shift in the position of the coin.

• A.
  $2.5\text{cm}$
• B. $2\text{cm}$
• C. $1.5\text{cm}$
• D. $3.5\text{cm}$

Answer 1

The correct option is D $3.5\text{cm}$

Apparent shift through a transparent medium of refractive index $\mu$ is given by $$s=t(1-\frac{1}{\mu })$$Where,
$t=$ thickness of the transparent medium.

According to problem, for first medium:
$t_1=8\text{cm},{\mu }_1=\frac{4}{3}$

So, shift due to first medium, $\Rightarrow s_1=t_1(1-\frac{1}{{\mu }_1})=8(1-\frac{1}{4/3})=2\text{cm}$

For second medium:
$t_2=4.5\text{cm},{\mu }_2=\frac{3}{2}$

so. shift due to this medium,

$\Rightarrow s_2=t_2(1-\frac{1}{{\mu }_2})=4.5(1-\frac{1}{3/2})=1.5\text{cm}$

Total shift is of the coin be
$S=s_1+s_2=2+1.5=3.5\text{cm}$

Hence, option (d) is the correct answer.

$\begin{array}{c}\text{Why this question?}\\ \text{To understand the difference between}\\ \text{apparent depth \& apparent shift.}\end{array}$