Question

The bottom of a container is of a $4.0cm$ thick glass slab. The container contains two immiscible liquids $A(\mu =1.4)$ and $B(\mu =1.3)$ of depths $6.0cm$ and $8.0cm$ respectively. What is apparent position of a scratch on the outer surface of the bottom of the glass slab when viewed through the container?

• A. 4.89 cm
• B. 2.79 cm
• C. 1.89 cm
• D. 5.39 cm

Answer 1

Answer: (A)

Let $m_1,m_2,m_3$ be the refractive index of glass slab, liquid $A$ and liquid $B$ respectively. The corresponding thickness are $t_1,t_2$ and $t_3$ respectively. The apparent position of the scratch on the outer surface is obtained by taking into account refraction at the three media and is given by
$=t_1\left(1-\frac{1}{{\mu }_1}\right)+t_2\left(1-\frac{1}{{\mu }_2}\right)+t_3\left(1-\frac{1}{{\mu }_3}\right)$
$=4\left(1-\frac{1}{1.5}\right)+6\left(1-\frac{1}{1.4}\right)+8\left(1-\frac{1}{1.3}\right)$
$=\frac{4\times 0.5}{1.5}+\frac{6\times 0.4}{1.4}+\frac{8\times 0.3}{1.3}$
= 1.33 + 1.71 + 1.85 = 4.89 cm