A ray inside glass of index meets a flat glass-to-air face at an angle of incidence of

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 inside glass of index 1.501.50 meets a flat glass-to-air face at an angle of incidence of 14.0∘14.0^\circ, the angle at which replacing sin⁡θ\sin\theta by θ\theta costs one per cent. ((a)) Find the relative error in replacing sin⁡14.0∘\sin 14.0^\circ by 14.0∘14.0^\circ in radians. ((b)) Find the refracted angle exactly from Snell's law and from its linearised form n1θ1=n2θ2n_1\theta_1 = n_2\theta_2, and the relative error of the linearised angle. ((c)) Which of the two one-per-cent statements, about the sine or about the refracted ray, does the 14∘14^\circ limit support?

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