A beam of unpolarized light of intensity I0 passes successively through three ideal polarizing sheets arranged as follows:
• Sheet A: transmission axis vertical.
• Sheet B: transmission axis at 45∘ to the vertical.
• Sheet C: transmission axis horizontal.
The sheets are separated by small air gaps that do not affect the polarization.
(a) Calculate the light intensity immediately after each sheet (after A, after B, after C). Express each result as a multiple of I0.
(b) Sheet B is now removed while Sheets A and C remain in place. Determine the final transmitted intensity and compare it to the value obtained in part (a).
(c) Provide a quantitative explanation for why including Sheet B increases the transmitted intensity even though it introduces an additional element that can block light.
(d) If Sheet B is rotated so that its transmission axis makes an angle ϕ with the vertical (with Sheet C still horizontal), obtain a general expression for the final transmitted intensity in terms of I0 and ϕ. State the value of ϕ that maximizes the transmitted intensity and give the corresponding maximum intensity.