A small air bubble in a glass sphere 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.
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Answer

`1.2 cm`

Explanation

Here, `mu_1 = 1, mu_2 = 1.5, R = -2 cm`
Incident ray `OA` in glass is refracted in air, along `AB`, and appears to come from `I`
`u = PO = ? B = PI = -1 cm`
As refractive 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.