Question

A beaker contains water up to a height $h_1$ and oil above water up to another height $h_2.$ Find the apparent shift in the position of the bottom of the beaker when viewed from above. Refractive index of water is ${\mu }_1$ and that of oil is ${\mu }_2.$

• A. $(1-\frac{1}{{\mu }_1})h_1+(1-\frac{1}{{\mu }_2})h_2$
• B. $(1-\frac{1}{{\mu }_1})h_1-(1-\frac{1}{{\mu }_2})h_2$
• C. $(1-\frac{1}{{\mu }_1})h_1+(1-\frac{1}{{\mu }_2})h_2$
• D. $(1-\frac{1}{{\mu }_1})h_1-(1-\frac{1}{{\mu }_2})h_2.$

Answer 1

The correct option is A $(1-\frac{1}{{\mu }_1})h_1+(1-\frac{1}{{\mu }_2})h_2$

The apparent shift of the bottom due to the water is
$△t_1=(1-\frac{1}{{\mu }_1})h_1$
and due to the oil is
$△t_2=(1-\frac{1}{{\mu }_2})h_2.$

The total shift = $△t_1+△t_2=(1-\frac{1}{{\mu }_1})h_1+(1-\frac{1}{{\mu }_2})h_2.$