Exemplar Problems

Problem 1 : Refraction at Spherical Surfaces

Problem Statement: A ray of light is incident on a spherical surface of radius (R) separating two media of refractive indices $$(n_1) and (n_2) ((n_2 > n_1)).$$ The ray is incident at the pole of the spherical surface. Calculate the position of the image formed by refraction.

Solution :

• Use the lens-maker’s formula for a spherical surface: $$\frac{1}{f} = (n_2 - n_1) \left(\frac{1}{R}\right).$$
• Step 2: Since the ray is incident at the pole, (f) is the object distance. Set (u = -f) (negative because it’s in the direction of the incident ray).
• Use the lens formula: $$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$$.
• Step 4: Solve for $v$ (image distance) using the given values of $n_1$, $n_2$, and $R$.
• Step 5: The negative sign for $u$ indicates that the object is on the opposite side as the incident ray.