A parallel beam of light is allowed to fall on a transparent spherical globe of diameter 30 cm and refractive index 1 . 5 . The distance from the centre of the globe at which beam of light can converge is _____ mm .

Step-by-step solution

For the refraction at the left surface, u = - ∞ ,   R = + 15   cm . μ 2 v - μ 1 u = μ 2 - μ 1 R ⇒ 1 . 5 v 1 - 1 - ∞ = 1 . 5 - 1 + 15 ⇒ v 1 = 45   cm For the refraction at the right surface, u = 45 - 30 = 15   cm ,   R = - 15   cm μ 2 v - μ 1 u = μ 2 - μ 1 R ⇒ 1 v 2 - 1 . 5 15 = 1 - 1 . 5 - 15 ⇒ v 2 = 7 . 5   cm Therefore, the distance from the centre where the beam will converge is, 15 + 7 . 5 = 22 . 5 &#1