(a) Two ideal polarizing sheet discs are placed together with their transmission axes crossed Perpendicularly so that no light is transmitted through the pair. However, when a third polarizing disc is inserted between them with its transmission axis at an angle of 45° relative to each of the other axes (as was demonstrated in class one day this term), light is now able to pass through. If unpolarized light of intensity Imax is incident on the first disc, calculate (as a fraction of Imax) the intensity of light that is transmitted through the three-disc combination.
(b) When light in vacuum is incident at the polarizing angle (Brewster's angle) on a certain glass slab, the angle of refraction is 31.8°. Calculate the values of:
(i) The polarizing angle, θp, of the glass;
(ii) Tthe index of refraction, n, of the glass.
(c) Light of wavelength 440 rim encounters a Young's double slit apparatus consisting of two identical slits (each one of width a) at a distance d apart from each other. After passing through the slits the light falls on to a relatively distant screen, yielding the pattern of intensity I plotted against deflection angle θ represented in the graph at the right. (Both double-slit interference and single-slit diffraction effects are at work here.)
Calculate:
(i) The slit width, a;
(ii) The slit separation, d;
(iii) The intensity of the m = 2 interference bright fringe, expressed as a decimal number (given correct to three significant figures) times Imax, where Imax is is the intensity of the m = 0 central bright fringe.