Question

Unpolarized light is passed through three successive Polaroid filters, each with its transmission axis at 45.0° to the preceding filter. What percentage of light gets through?

Answer 1

Answer:

The percentage is  $k = 12.5 \%$

Explanation:

From the question we are told that

    The  axis is is  at  $\theta = 45 ^o$

Generally the of intensity light emerging from the first polarizer is mathematically represented as

                $I_{1} = \frac{I_o}{ 2}$

Where  $I_o$ is the intensity of unpolarized light

       Now the light emerging from the second polarizer is mathematically represented as

         $I_2 = I_ 1 * cos ^2(\theta )$

         $I_2 = \frac{I_o}{2} * cos ^2(45 )$

        $I_2 = \frac{I_o}{2} * \frac{1}{2} = \frac{I_o}{4}$

  Now the light emerging from the third  polarizer is mathematically represented as      

       $I_3 = I_ 2 * cos ^2(\theta )$

       $I_3 = \frac{I_o}{4} * cos ^2(45 )$

      $I_3 = \frac{I_o}{8}$

Now the percentage of the intensity of light that emerged with respect to the intensity of  the unpolarized light is

      $k = \frac{\frac{I_o}{8} }{I_o } * 100$

     $k = 12.5 \%$