Question

An air bubble is trapped at point B (CB = 20 cm) in a glass sphere of radius 40 cm and refractive index 1.5 as shown in figure. Find the nature and position of the image of the bubble as seen by an observer at point P.

Answer 1

Radius of the glass sphere, R = 40 cm

Refractive index, μ₁ = 1.5 of glass

Distance of the bubble from the centre of the sphere = 20 cm

Refractive index of air = 1

`mu_2/v - mu_1/u = (mu_2 - mu_1)/R`

⇒ `1/v - 1.5/-20 = (1 - 1.5)/-40`

⇒ `1/v + 1.5/20 = (-0.5)/(-40)`

⇒ `1/v + 3/40 = 1/80`

⇒ `1/v = 1/80 - 3/40`

⇒ `1/v = (1 - 6)/80`

= `(-5)/80`

= `-1/16`

⇒ v = −16

So, the image formed is virtual.