A mixture of plane polarised and unpolarised light falls normally on a polarising sheet. On rotating the polarising sheet about the direction of the incident beam, the transmitted intensity varies by a factor 4. Find the ratio of the intensities `I_(P)` and `I_(0)` respectively of the polarized and unpolarised components in the incident beam. Next the axis of polarising sheet is fixed at an angle of `45^(@)` with the direction when the transmitted intensity is maximum. Then obtain the total intensity of the transmitted beam in terms of `I_(0)`.
`[(3)/(2),(5I_(0))/(4)]`

Options

A. `(2)/(1)`
B. `(3)/(2)`
C. `(4)/(3)`
D. `(4)/(1)`

Answer

2

Explanation

Intensity of polarised light
`I__(p) = I_(p) cos ^(2) theta//2`
`theta I_(p) ={ {:(,"max" =I_(p)),(,"min"=0):}`
But intensity of unpolarised light remains const.
`therefore I_(0) = I_(0)//2`
`therefore I_("max")= I_(p) + I_(0)//2`
`I_("min") = I_(0)//2`
but problem `I_(p) +(I_(0))/(2) = 4(I_(0))/(2)`
`therefore (I_(p))/(I_(0)) =(3)/(2)`