A beam of light of intensity I0 is linearly polarized such that its electric-field vector makes an angle of 30∘ above the horizontal. The beam encounters two ideal polarizing sheets in succession as it travels toward a photodetector. The transmission axis of the first sheet is horizontal, and the transmission axis of the second sheet is oriented at an angle θ above the horizontal.
Respond to every part clearly, showing all reasoning and any calculations.
(a) Determine the intensity I1 of the beam immediately after passing through the first polarizing sheet.
(b) Express the transmitted intensity I2 after the second sheet in terms of I1 and θ.
(c) For what value of θ is I2 equal to one-fourth of I0? Show all steps.
(d) Describe physically why, for θ=90∘, essentially no light is detected even though each individual sheet transmits 50\% of the unpolarized light incident upon it.