Light from an ordinary source (say a sodium lamp) is passed through a polaroid sheet `P_(1)`. The transmitted light is then made to pass through a second polaroid sheet `P_(2)` which can be rotated so that the angle `theta` between the two polaroid sheets varies from `0^(@)` to `90^(@)`. Show graphically the variation of intensity of light transmitted by `P_(1)` and `P_(2)` as a function of angle `theta`. Take incident beam intensity `I_(0)`. Why does light from clear blue portion of sky show a rise and fall of intensity when viewed through a polaroid which is rotated ?

Explanation

When incident beam intensity from an ordinary source is `I_(0)`, beam intensity of polarised light from `P_(1)` is `I_(0)//2`. If `theta` is angle between `P_(1)` and `P_(2)`, then according to law of Malus, intensity of polarised light from `P_(2)` is
`I = (I_(0))/(2) cos^(2) theta`
When `theta = 0^(@)`, `I = (I_(0))/(2) cos^(2) theta = ((I_(0))/(2))`
When `theta = 30^(@)`, `I = (I_(0))/(2) cos^(2) 30^(@) = (3)/(4)((I_(0))/(2))`
When `theta = 45^(@)`, `I = (I_(0))/(2) cos^(2) 45^(@) = (1)/(2)((I_(0))/(2))`
When `theta = 60^(@)`, `I = (I_(0))/(2) cos^(2) 60^(@) = (1)/(4)((I_(0))/(2))`
When `theta = 90^(@)`, `I = (I_(0))/(2) cos^(2)90^(@) = Zero`
The variation of `I` with `theta` is plotted in Fig.
The blue colour of sky is due to scattering. Light from clear blue portion of sky polarised by scattering. The polaroid through which this light is observed atcs as analyser. The intensity of light viewed through rotating polaroid varies as per law of Malus.