Question

A glass sphere of radius $15cm$ has a small bubble $6cm$ from it centre. The bubble is viewed along a diameter of the sphere from the side o which it lies. How far from the surface will it appear to be if the refractive index of glass is $1.5$?

Answer 1

We know that,

Refractive Index of the glass${\mu }_1=1.5$

Refractive Index of the air ${\mu }_2=1$

Radius of the Convex surface $r=-15cm$

Real Depth of the Air Bubble $u=-6cm$

Let the Apparent Depth of the Air bubble $=vcm$

By using formula for refraction on the curved surface

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

$\frac{1}{v}-\frac{1.5}{-6}=\frac{1-1.5}{-15}$

$\frac{1}{v}=\frac{0.5}{-15}+\frac{1.5}{-6}$

$\frac{1}{v}=\frac{-1}{30}-\frac{1}{4}$

$v=\frac{-120}{34}$

$v=\frac{-60}{17}$

$v=-3.5cm$

Hence, the image is formed at the distance of -$3.5cm$ from the surface