Question

A hemispherical glass body of radius $10cm$ and refractive index 1.5 is silvered on its curved surface. A small air bubble is $6cm$ below the flat surface inside it along the axis. The position of the image of the air bubble made by the mirror is seen:

• A. $14cm$ below flat surface
• B. $20cm$ below flat surface
• C. $16cm$ below flat surface
• D. $30cm$ below flat surface

Answer 1

The correct option is B $20cm$ below flat surface

Mirror formula gives :

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}\Rightarrow \frac{1}{v}+\frac{1}{-4}=\frac{1}{-5}$

$⟹v=20cm$

Image will form $10+20=30cm$ below the flat surface.

Now,

$\frac{ApparentDepth}{RealDepth}$ = $\frac{RefractiveIndexofAir}{RefractiveIndexofMedium}$

$⟹h_a=h_r\frac{{\mu }_1}{{\mu }_2}=30\times \frac{1}{1.5}=20cm$