Two poalroids are placed at `90^(@)` to eachother and the transmitted intensity is zero. What happens when one more polaroid is placed between these two bisecting the angle between them ? What will be the diraction of polarization of outcoming beam ?

Explanation

The situation is shown in the figure. When a third Polaroid is placed between the two Polaroid, the transmission axis of Polaroid 3 will make an angle of `45^(@)` is clockwise direction,
The intensity of the transmitted light through Polaroid 3 is `I_(3)=l_(0)cos^(2) 45^(@)=(I_(0))/(2)`
When this plane polarised light of intensity `(I_(0)//2)` is incident on the polaroid 2, the intensity of the transmitted polarised wave will be
  `I_(2)=I_(2)cos^(2) 45^(@)=(I_(0))/(2)cos 45^(@)=(I_(0))/(4)` , here `l_(0)` is the intensity of polarised light after passing through polariser 1.