A thin walled glass sphere of radius 2.5 cm is filled with water. An object (O) is placed at 7.5 cm from the surface of the sphere. Neglecting the effect of glass wall, at what distance the image ( I ) of the object, measured from the centre of sphere is formed?

Step-by-step solution

For refraction at first surface, u=-7.5 ~cm , R₁=2.5 ~cm ₁=1, ₂= 4 3 ₂ v^ - ₁ u = ₂- ₁ R₁ 4 / 3 v^ - 1 (-7.5) = 4 / 3-1 25 4 3 v^ = 1 7.5 - 1 7.5 =0 v^ = It means the ray is parallel within the sphere. For refraction at second surface, u=- , ₁= 4 3 ₂=1, R₂=-2.5 ~cm ₂ v^ - ₁ u = ₂- ₁ R₂ gives 1 v^ - 4 / 3 (- ) = 1-(4 / 3) (-2.5) v=+7.5 ~cm i.e. Image is formed at distance 7.5 cm to the right of P₂ . Hence, distance of final image P from centre C=7.5+2.5=10 ~cm .