Refraction Formula For Spherical Surface — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
Refraction Formula for Spherical Surface Valid for refraction at a single spherical interface between two transparent media. Assumes paraxial rays (small aperture) and requires strict adherence to Cartesian sign convention. Apply Snell's Law at the point of incidence: n1 sin(i) = n2 sin(r). Use small angle approximation: sin(x) ≈ tan(x) ≈ x (radians). Use exterior angle theorem in triangles formed by object, image, center of curvature, and point of incidence. Relate angles to heights and object/image distances (α ≈ h/u, etc.), applying sign conventions. Light rays must be paraxial (close to the principal axis). Aperture of the spherical surface must be small relative to radii. Sign convention: Light travels L->R. Distances measured from Pole. Direction of light is positive. Absolute refractive indices must be used. Confusing μ₁ (medium of incident ray) and μ₂ (medium of refracted ray). Forgetting the sign of R (positive for convex towards rarer medium if light incident from rarer, but strictly depends on geometry). Assuming u is always negative (true for real objects, but positive for virtual objects). Applying this formula for plane surfaces (where R → ∞, though it works if R is set to infinity).