A parallel beam of light travelling in air (refractive index 1.0) is incident on a convex spherical glass surface of radius of curvature 50 cm. Refractive index of glass is 1.5. The rays converge to a point at a distance x ~cm from the centre of the curvature of the spherical surface. The value of x is _ _ _ _ cm.

Step-by-step solution

For refraction at a single spherical surface, we use the formula: ₂ v - ₁ u = ₂ - ₁ R Given data: Refractive index of air ₁ = 1.0 Refractive index of glass ₂ = 1.5 Radius of curvature R = +50 cm (convex surface) Object is at infinity for a parallel beam, so u = - Substituting the values: 1.5 v - 1.0 - = 1.5 - 1.0 50 1.5 v - 0 = 0.5 50 1.5 v = 1 100 v = 1.5 100 = 150 cm The image is formed at a distance of 150 cm from the pole (vertex) of the spherical surface. The question asks for the distance x from the centre of