At a refraction the paraxial approximation replaces by ; the leading discarded term is
PHYSICS · Subjective · Fermi University Physics · Optics & Photonics · Geometrical optics and imaging · Geometrical optics and imaging
What an Instrument Can See, Ch The paraxial system as an operator
Problem
At a refraction the paraxial approximation replaces sinθ by θ; the leading discarded term is −θ3/6, so the fractional error in the linearised sine grows approximately as θ2/6. At a flat surface, where the angle of incidence equals the ray's angle to the axis, estimate the marginal ray angle θ (in radians and in degrees) at which this fractional error reaches 5%, and give the equivalent f-number using N=1/(2tanθ), the relation between semi-aperture angle and f-number for a lens imaging an object at infinity.