(a) consider an electromagnetic wave of the form e eolicos(kz - wt)0.8j sin(kz - wt + ¢) _ (i) discuss the effect of the phase d on the state of polarisation of the wave. (ii) for what value(s) of the phase 0 is this wave linearly polarised? (ii we pass that field through a half-wave plate. for the phase value you obtained in (ii), at what relative angle polarisation state into 'horizontal' (0°)? explain your answer. must the axis of this half-wave plate be oriented to turn the (b) (advanced) a sheet of plastic, uniformly 1.5 mm polarizers which are illuminated from the back with 532 nm bright bands appears. how much does the relative difference in the index of refraction in the plastic (nn1) have to vary in order to produce the half-wave plate behaviour needed to create successive dark and bright bands? show all working thick, is viewed between crossed linear light.

Your starship, the aimless wanderer, lands on the mysterious planet mongo. as chief scientist-engineer, you make the following measurements: a 2.50-kg stone thrown upward from the ground at 14.0 m/s returns to the ground in 5.70 s ; the circumference of mongo at the equator is 2.20×10^5 km ; and there is no appreciable atmosphere on mongo. (a) the starship commander, captain confusion, asks for the following information: what is the mass of mongo? (b) if the aimless wanderer goes into a circular orbit 2.20×10^4 km above the surface of mongo, how many hours will it take the ship to complete one orbit? (c) an unmanned spacecraft is in a circular orbit around the moon, observing the lunar surface from an altitude of 44.0 km . to the dismay of scientists on earth, an electrical fault causes an on-board thruster to fire, decreasing the speed of the spacecraft by 23.0 m/s . if nothing is done to correct its orbit, with what speed (in km/h) will the spacecraft crash into the lunar surface?