Two transparent media A and B , having refractive indices 1.33 and 1.48 respectively, are separated by a spherical surface of radius 30 cm . Medium A lies on the convex side of this surface. At what distance from the separating surface should a point object be positioned in medium A to ensure that paraxial rays emerge parallel following refraction at the surface?

Step-by-step solution

For refraction at a single spherical surface, the formula is given by: n₂ v - n₁ u = n₂ - n₁ R Given that the object is in medium A , n₁ = 1.33 and n₂ = 1.48 . Since medium A lies on the convex side of the surface, the surface is convex towards the incident light. Therefore, the center of curvature lies in medium B , making the radius of curvature positive: R = +30 cm . The paraxial rays emerge parallel after refraction, which means the image is formed at infinity, so v = . Substituting the values into the formula: