Question

A beam of light is a mixture of unpolarized light with intensity Ia and linearly polarized light with intensity Ib. The polarization direction for the polarized light is vertical. When this mixed beam of light is passed through a polarizer that is vertical, the transmitted intensity is 16.8 W/m2; when the polarizer is at an angle of 55.0° with the vertical, the transmitted intensity is 8.68 W/m2. (a) Is Ia greater than, less than, or equal to Ib? Explain. (b) Calculate for both intensities.

Answer 1

In the first situation all of the polarized light is transmitted but only half of the unpolarized light makes it through the filter. If we use A for the intensity of the polarized light (i.e.   I _p )    and B for I_u   we can write:

    A + 0.5B = 16.8

Now when the polarizer is at an angle of 55 deg, we get cos²55 = 0.329 of the polarized light through, while we still get half of the unpolarized light.So:

   0.329A + 0.5B = 8.68

If you subtract the equations:

     0.671 A =8.12    or    A = 12.94 W/m²    for the original intensity of polarized light

And:    12.94   + 0.5B =16.8   so    B = 7.72W/m²