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I came across a question in my Textbook which I am unsure about.

Two polarising filters are aligned to transmit vertically polarised light. They are held in front of a source of horizontally polarised light. The filter closest to the light source is rotated by 45 degrees. The intensity of the light passing through the filters:
A does not change
B increases
C increases to maximum intensity
D decreases

The answer given is option B, however I don't understand why the intensity increases?

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    $\begingroup$ Ask yourself: what is the polarisation after the light passes the first filter? $\endgroup$ – my2cts Nov 22 '20 at 11:35
  • $\begingroup$ @my2cts Initially no light will pass through the first filter as it is vertically polarised, therefore the intensity is zero, however, once the filter is rotated some light passes through the filter so the intensity increases. Is this correct? $\endgroup$ – E C Nov 22 '20 at 16:39
  • $\begingroup$ How much light passes the first filter after rotation and what US it's polarisation? $\endgroup$ – my2cts Nov 22 '20 at 21:58
  • $\begingroup$ Half the light? @my2cts $\endgroup$ – E C Nov 22 '20 at 22:07
  • $\begingroup$ So what happens next? $\endgroup$ – my2cts Nov 22 '20 at 22:08
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This is easily explained using Malus' law, $I=I_0cos^2\theta$, where $I$ is the transmitted intensity, $I_0$ is the initial intensity and $\theta$ is the angle between the pass axis of the polarizer and the polarization axis of light. Supposing the first filter to have been rotated by 45 degrees, we have $I_1=\frac{I_0}{2}$. Since the final filter now makes an angle of 45 with the second one, $I_2=I_1cos^245^o=\frac{I_0}{4}>0$, representing an increase.

The point is that the polarization of light changes after passing through the first polarizer-which is to say, it changes from horizontal to a 45 degree one (which in turn makes it 45 degrees with respect to the second polarizer). Had it been that (half) the light passes through the first polarizer and remains horizontally polarized, we would have retained the intuitive result that the final transmitted intensity is zero.

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  • $\begingroup$ Is it correct to say, in simple terms, that if the filter hadn't been rotated 45 degrees, there would be no light passing through the filter, so no intensity either. Once the filter has been rotated 45 degrees, some light is transmitted, therefore the intensity increases? $\endgroup$ – E C Dec 1 '20 at 18:28
  • $\begingroup$ @EC-Yes, you are right. $\endgroup$ – A.D. Dec 2 '20 at 5:56

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