When an unpolarized light passes through a polariser, the intensity of the emergent light from the polariser depends on the square of the cosine of the angle between the plane of the polariser and the direction of the incident light.
The formula to calculate the intensity (I1) of the emergent light from a polariser which makes an angle θ with the direction of the incident light is given by
I1=Icos2θ..................(1)
where, I is the intensity of the incident light.
Substitute 45∘ for θ into equation (1) to obtain the intensity of the first emergent light.
I1==Icos245∘2I
In a similar manner, the intensity (I2) of the second emergent light can be written as
I2====I1cos245∘2I14I22I
Thus, for n number of such polarisers, the net intensity (In) of the emergent light can be written as
In=2nI......................(1)
Comparing equation (1) with the given expression for the intensity, it can be concluded that
n=6