A parallel beam of light travelling in air (refractive index 1.0 ) is incident on a convex spherical

Question

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 $x \mathrm{~cm}$ from the centre of the curvature of the spherical surface. The value of $x$ is $\_\_\_\_$ cm.

Professor PC Thomas Classes · Answer

Using the refraction formula for a single spherical surface $\frac{\mu_2}{v} - \frac{\mu_1}{u} = \frac{\mu_2 - \mu_1}{R}$. Since the incident beam is parallel, $u = \infty$. Given $\mu_1 = 1$, $\mu_2 = 1.5$, and $R = +50	ext{ cm}$. Substituting the values gives $\frac{1.5}{v} - 0 = \frac{1.5 - 1}{50} \Rightarrow \frac{1.5}{v} = \frac{0.5}{50} \Rightarrow v = 150	ext{ cm}$. The distance of the focal point from the pole is 150 cm. The distance from the center of curvature is $x = v - R = 150 - 50 = 100	ext{ cm}$.