Unpolarized light of intensity I0 is incident on a series of three polarizing filters. The axis of the second filter is oriented at 45o to that of the first filter, while the axis of the third filter is oriented at 90o to that of the first filter. What is the intensity of the light transmitted through the third filter

The intensity of the light transmitted through the third filter is  

Explanation:

From the question we are told

   The intensity of the unpolarised light

   The angle between the first and second polarizer is  

     The angle between the first and third  polarizer is  

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

According to Malus law the intensity of light emerging from the second polarizer is mathematically represented as

Substituting for and

According to Malus law the intensity of light emerging from the third polarizer is mathematically represented as

Substituting for and

i think it because equal matrices have equal dimensions, only square matrices can be symmetric. for all indices and . every square diagonal matrix is symmetric, since all off-diagonal elements are zero. in linear algebra, a real symmetric matrix represents a self-adjoint operator over a real inner product space.