Question

An air bubble 'A' is trapped inside a glass sphere of radius CP$=10$cm at a distance of $4.0$cm from its centre 'C'. Where does it appear to an observer O(see figure) who is looking at it along the diameter from the side to which it is nearest? [Refractive Index of glass $=1.5$).

Answer 1

Given: An air bubble 'A' is trapped inside a glass sphere of radius CP=10cm at a distance of 4.0cm from its centre 'C'. If an observer O(see figure) who is looking at it along the diameter from the side to which it is nearest

To find the distance of the bubble from the surface of the sphere.

Solution:

As per the given criteria,

Refractive index of the glass sphere, ${\mu }_1=1.5$

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

object distance from the surface, $u=-(10-4)=-6cm$, as the bubble is 4.0cm from its centre.

Radiusof the sphere, $R=-10cm$

Using the formula for refraction on the curved surface, we get

$\frac{{\mu }_2}{v}-\frac{{\mu }_1}{u}=\frac{{\mu }_2-{\mu }_1}{R}⟹\frac{1}{v}-\frac{1.5}{(-6)}=\frac{1-1.5}{(-10)}⟹\frac{1}{v}=\frac{0.5}{10}-\frac{1.5}{6}⟹\frac{1}{v}=\frac{(0.5\times 6)-(1.5\times 10)}{60}=\frac{12}{60}⟹v=-5cm$

Hence the air bubble appear at a distance of 5cm from the survace to the observer.