If the angle between the pass axis of polarizer and the analyser is 45º, write the ratio of the intensities of original light and the transmitted light after passing through the analyser.
I = Im cos2 θ
I is the transmitted intensity
Imis the maximum value of the transmitted intensity
θ is the angle between the two polarising directions
`l/l_m = cos^2 theta`
`I/I_m = cos^2 45° = (1/sqrt2)^2`
`I/I_m = 1/2`