At what angle should the axes of two polaroids be placed so as to reduce the intensity of incident unpolarized light to `1//3`.

Answer

`35.3^(@)`

Explanation

The first polariser polarises the unpolarised light reducing its intensity from `I_(0)` to `I_(0)//2`. We have toreduce the intensity from `I_(0)//2` to `I_(0)//3`.
According to Law of Malus, `I = I_(0) cos^(2) theta`
`cos^(2)theta = (I)/(I_(0)) = (I_(0)//3)/(I_(0)//2)` ,
`cos theta = sqrt((2)/(3)) = sqrt(0.6667) = 0.8165`
`theta = cos^(-1) (0.8165) = 35.3^(@)`