Working from another optics text

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Wave propagation and light in media · Polarisation and anisotropic media

What an Instrument Can See, Ch The boundary as a two-port

Problem

Working from another optics text, someone writes the p-polarisation reflection coefficient for light travelling from a medium of index nin_i into a medium of index ntn_t, with incidence angle θi\theta_i and transmission angle θt\theta_t related by Snell's law, as rp=ntcos⁡θi−nicos⁡θtntcos⁡θi+nicos⁡θt.r_p = \frac{n_t\cos\theta_i - n_i\cos\theta_t}{n_t\cos\theta_i + n_i\cos\theta_t}. Using this for light going from air (ni=1.00n_i = 1.00) into water (nt=1.33n_t = 1.33) at θi=40.0°\theta_i = 40.0° (so θt=28.9°\theta_t = 28.9° by Snell's law), they compute rp=+0.076r_p = +0.076 and conclude that the p and s coefficients simply carry opposite signs at this angle, with no further consequence. ((a)) Apply the quoted formula at normal incidence (θi=θt=0\theta_i = \theta_t = 0) and show that it contradicts a relation that must hold at every interface in the chapter's sign convention, in which rs=rpr_s = r_p at normal incidence. Name the relation. ((b)) State the error, give the corrected expression for rpr_p in that convention, and recompute its value at θi=40.0°\theta_i = 40.0°.

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