Question

Unpolarized light is passed through three successive polarizing filters, each with its transmission
axis at 45deg to the preceding filter. What percentage of the total light striking the first filter gets
through the last filter? Does the transmission depend on wavelength? Explain.

Answer 1

According to one half rule, when an depolarized light meet the polarizer the intensity of transmitted light equal to the half intensity of depolarized light.  

So, if we take intensity "I", after first polarizer it changed to "I/2".

According to malus law, when a plane polarized light meet a polarizer the intensity of transmitted light is directly proportional to square of cosine of angle between the optic axis of polarizer

So intensity after second polarizer = I/2×cos²45 ​​

= I/2 × (1/root 2)² cos 45 = 1/ root 2

=I /4

intensity after third polarizer = I/4 ×cos²45

= I/8

percentage of light striking the first filter get through the last filter is = final intensity / total intensity ×100 = (I/8÷I )×100

= 1/8 ×100

=12.5%

The polarization means that restricting electric field vibration of light into single plane. The intensity change during polarization doesn't depend on wavelength of light used means that transmission doesn't depend wavelength.