A beam of unpolarized light passes sequentially through two ideal polarizing filters

PHYSICS · Single correct · A Level · Physics · Waves · Waves

Problem

A beam of unpolarized light passes sequentially through two ideal polarizing filters. The transmission axis of the first filter is vertical; the second is oriented 45∘45^{\circ} to the vertical. Which statement best accounts for the reduction in transmitted intensity? (a) The first filter produces vertically polarized light; since the second is only 45∘45^{\circ} away, about cos⁡45∘ ⁣≈ ⁣70%\cos 45^{\circ}\!\approx\!70\% of the light’s intensity still passes, so the reduction is only moderate. (b) Because the second filter is not parallel to the first, it blocks the vertically polarized light completely, and essentially no light is transmitted. (c) The first filter produces vertically polarized light, and only the component of that light aligned with the 45∘45^{\circ} transmission axis of the second filter passes, so the intensity is reduced by an additional factor of cos⁡245∘\cos ^2 45^{\circ}.},{ (d) Only the relative angle between the filters matters, so the intensity after the pair is I=I0cos⁡245∘=0.5I0I=I_{0}\cos^{2}45^{\circ}=0.5I_{0}; the first filter does not further reduce the beam.

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