All matrices below are multiplied right to left in the order light meets the elements…

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Optics & Photonics · Polarisation and anisotropic media

Optics and Photonics, Ch Polarisation states, polarisers and the Jones and Stokes calculus

Problem

All matrices below are multiplied right to left in the order light meets the elements (the rule of Chapter 1). ((a)) A converging thin lens of focal length f1=15 cmf_1=15\text{ cm} and a diverging thin lens of focal length f2=−30 cmf_2=-30\text{ cm} lie in contact in air (n=1n=1). A paraxial ray leaves an object with height y0=3.0 mmy_0=3.0\text{ mm} and angle θ0=0.020 rad\theta_0=0.020\text{ rad}, meeting lens 1 first, then lens 2. Find the ray's height and angle after lens 2. ((b)) Light linearly polarised along xx, Jones vector (1,0)(1,0), meets an ideal linear polariser at θ1=20∘\theta_1=20^\circ first, then one at θ2=70∘\theta_2=70^\circ. Find the output irradiance relative to the input. ((c)) A sheet of crown glass (n=1.50n=1.50) reflects unpolarised light at Brewster's angle; the reflected beam of total irradiance Itot=2.00I_{\text{tot}}=2.00 (arbitrary units) is purely ss-polarised. A polariser at 0∘0^\circ, 45∘45^\circ, 90∘90^\circ, 135∘135^\circ to the plane of incidence transmits I0∘=0I_{0^\circ}=0, I45∘=1.00I_{45^\circ}=1.00, I90∘=2.00I_{90^\circ}=2.00, I135∘=1.00I_{135^\circ}=1.00. Write the Stokes vector and degree of polarisation. ((d)) Two coherent beams of the same polarisation, E1=5.0E_1=5.0 and E2=2.0E_2=2.0 (arbitrary units), phase difference δ=60∘\delta=60^\circ, arrive together. Find the resultant irradiance by phasor addition and compare with the simple sum of irradiances.

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