A ray travels in air parallel to the axis at height and meets a spherical…
PHYSICS · Multi-part · 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
A ray travels in air parallel to the axis at height h=20mm and meets a spherical air-to-glass surface of radius R=+50mm; the glass has index n=1.50. Its angle to the axis is zero, yet the paraxial matrix may still be poor for it.
((a)) Find the angle of incidence at the surface.
((b)) Use Snell's law exactly to find the refracted ray's angle to the axis inside the glass.
((c)) Find the same angle from the refraction matrix, and the percentage by which the matrix value falls short of the exact one.
((d)) Below what height does the angle of incidence stay under the 14.0 degrees at which the sine's error reaches one per cent?