Question

A parallel beam of light travelling in water (µ = 4/3) is refracted by a spherical air bubble of radius 2 mm placed in water. Assume that the light rays to be paraxial. 

(a) Find the position of the image due to refraction at the first surface and the position of the final image. 

(b) Draw a ray diagram showing the positions of both images.

Answer 1

The image of the object formed by the first refraction by the water-glass surface acts as the object for the second refraction at glass-water surface. 

(a) For the refraction from a single spherical surface, we have

Let P₁ be pole at the first surface and P₂ to be pole at the second surface. At P,

The first surface will form a virtual image I₁ at a distance 0.6 cm to the left of P₁ as shown in the figure. This image acts as an object for the second surface. So for the second surface at P₂ ,

The final image I₂ is formed at a distance of 0.5 cm to the left of the second surface P₂ . The final image is at a distance of 0.5 - 0.4 = 0.1 cm to the left of the first surface as shown in figure. 

(b) The ray diagram is already shown in the figure drawn.