Question

A parallel beam of light travelling in water (refractive index $=4/3$) is refracted by a spherical air bubble of radius 2 mm situated in water. Assuming the light rays to be paraxial, Find out the distance between a final image from the centre of the bubble in mm.

Answer 1

Given: A parallel beam of light travelling in water (refractive index =4/3) is refracted by a spherical air bubble of radius 2 mm situated in water.

To find the the distance between a final image from the centre of the bubble in mm, by assuming the light rays to be paraxial

Solution:

Considering the refraction at the first surface (with O as origin, left -ve, right +ve) we get,

$\frac{1}{v}-\frac{\mu }{-\infty }=\frac{1-\mu }{R}⟹v=-\frac{R}{\mu -1}$

The image of the distant object formed by the first surface is S'. This serves as object for the second surface. WE have now (with reference to O' as origin, left -ve and right +ve).

$\frac{\mu }{v}-\frac{1}{-(\frac{R}{\mu -1}+2R)}=\frac{\mu -1}{-R}⟹v=-\left(\frac{2\mu -1}{\mu -1}\right)R$

Thus the final image is at a distance $\left(\frac{2\mu -1}{\mu -1}\right)R$ from O' to the left or $\left(\frac{2\mu -1}{\mu -1}\right)R-R=\frac{\mu }{\mu -1}R$ to the left from the center.

Here the distance of the image from the center = $\frac{\frac{4}{3}}{\frac{4}{3}-1}\times 2=8mm$