(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 I_max is incident on the first disc, calculate (as a fraction of I_max) 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, θ_p, 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 I_max, where I_max is is the intensity of the m = 0 central bright fringe.