Question

At what angle should the axes of two Polaroids be placed so as to reduce the intensity of the incident unpolarized light to 1515.

Answer 1

Complete  Question

At what angle should the axes of two Polaroids be placed so as to reduce the intensity of the incident unpolarized light to 1/5.

Answer:

The  angle is  

Explanation:

From the question we are told that

   The light emerging from second Polaroid is 1/5 the  unpolarized

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

             $I_1 = \frac{I_o}{ 2 }$

Generally from the Malus law the intensity of light emerging from the second Polaroid  is mathematically represented

      $I_2 = I_1 cos^2 (\theta )$

=>   $cos^2 (\theta ) = \frac{I_2}{I_1 }$

=>   $cos (\theta) = \sqrt{ \frac{I_2}{I_1} }$

From the question $I_2 = \frac{I_o}{5}$

     $cos (\theta) = \sqrt{ \frac{ \frac{ I_o}{5} }{\frac{I_o}{2} } }$

     $cos (\theta) = \sqrt{ \frac{2}{5} }$

=>    $\theta = cos ^{-1} [\sqrt{\frac{2}{5}} ]$

=>    $\theta = 50.77^o$