Question

A glass sphere $(\mu =1.5)$ of radius $20cm$ has a small air bubble $4cm$ below its center. The sphere is viewed from outside and along a vertical line through the bubble. The apparent depth of the bubble below the surface of sphere is (in cm) :

• A. $13.33$
• B. $26.67$
• C. $15$
• D. $30$

Answer 1

The correct option is B $26.67$

concept: It is the case of refraction through curved surface formulae used

$\frac{{\mu }_2}{v}-\frac{{\mu }_1}{u}=\frac{{\mu }_2-{\mu }_1}{R}$

Given: ${\mu }_2=1$, ${\mu }_1=1.5$

$R=-20$

Object distance$=u=-(20+4)=-24$

Here apparent depth is image distance which is v

$\frac{1}{v}-\frac{1.5}{-24}=\frac{1-1.5}{-20}$

$\Rightarrow \frac{1}{v}=\frac{1}{40}-\frac{1}{16}=\frac{-3}{80}$

$\Rightarrow v=-\frac{80}{3}=-26.67$

Hence bubble looks at depth of $26.67$.