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 :
- Step 1: 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).
- Step 3: 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 n1, n2, and (R).
- Step 5: The negative sign for (u) indicates that the object is on the same side as the incident ray.
BETA
