Natural light falls on a system of three identical in-line Polaroids the principle direction of the middle Polaroid forming an angle `varphi = 60^(@)` with those of two other Polaroids. The maximum transmission coefficient of each Polaroid is equal to `tau = 0.81` when plane-polarized light falls on them. How many times will the intensity of the light decrease after its passing through the system?

Explanation

When natural light is incident on the first polaroid, the fraction transmitted will be `(1)/(2)tau` (only the component polarized parallel to the principle direction of the polaroid will go). The emergent light will be plane polarized and on passing through the second polaroid will be polarized in a different direction (corresponding to the principle direction of the `2^(nd)` polaroid) and the intensity will have decreased further by `tau cos^(2) varphi`.
In the third polaroid the direction of polarization will again have to change by `varphi` thus only a fraction `tau cos^(2) varphi` will go through.
Finally `I = I_(0) xx (1)/(2) tau^(3) cos^(4) varphi`
Thus the intensity will have decreased
`(I_(0))/(I) = (2)/(tau^(3)cos^(4)varphi) = 60.2` times
for `tau = 0.81, varphi = 60^(@)`.