Question

A small air bubble in glass shpere of radius `2 cm` appears to be `1 cm` from the surface when looked at, along a diameter. If the refractive index of glass is `1.5`, find the true position of the air bubble.

Answer 1

Correct Answer - `1.2 cm`
Here, `mu_(1), mu_(2) = 1.5, R = - 2cm`
Incident ray `OA` in glass is refracted in air, along `AB`, and appears to some from `I`.
`u = PO = ? v = PI = - 1 cm`
As refraction occurs from denser to rarer medium,
`:. -(mu_(2))/(u) + (mu_(1))/(v) = (mu_(1) - mu_(2))/(R )`
`-(1.5)/(u) + (1)/(-1) = (1 - 1.5)/(-2) = (1)/(4)`
`(1.5)/(u) = -1 - (1)/(4) = -(5)/(4)`
`u = (-4 xx 1.5)/(5) = - 1.2 cm`
The air bubble `O` lies at `1.2 cm` from the refracting surface within the sphere.