In a laboratory investigation, a beam of unpolarized laser light is directed at two identical ideal polarizing sheets. The first sheet has its transmission axis fixed vertically. The second sheet can be rotated so that its transmission axis makes an angle θ with the vertical. A photodetector placed after the second sheet measures the transmitted light intensity I(θ). When θ=50∘, the detector reads 0.30mWcm−2.
(a) Derive an expression for I(θ) in terms of the initial intensity I0 of the laser beam and the angle θ.
(b) Use your expression to determine the initial intensity I0 of the laser beam.
(c) For what angle θ will the detector reading be exactly 0.10I0?
(d) Suppose the first polarizing sheet is replaced with a non-ideal sheet that transmits only 80\% of the light that would be transmitted by an ideal sheet with the same orientation. All other conditions remain unchanged. Recalculate the detector reading at θ=50∘ and explain any differences from the ideal-sheet case.