Question

A glass sphere of radius $15$ cm contains a small air bubble at a distance $6$ km from its centre when viewed along its diameter from the nearest side,

Answer 1

Let the Apparent Depth of the Air bubble (or the distance of the image of the bubble from the air surface) $=vcm$.

When the light from the bubble goes from the glass to the air, then

$\mu ₂/v-\mu ₁/u=(\mu ₂-\mu ₁)/r$

$1/v-1.5/-3=(1.5-1)/-5$

$1/v+1/2=0.5/-5$

$1/v=-1/2-1/10$

$1/v=(-5-1)/10$

$1/v=-6/10$

$v=-10/6cm.$

$v=-5/3$

$v=-1.67cm$

Hence, the image is formed at the distance of $1.67$ cm from the convex surface.