Two polaroids are placed at `90^(@)` to eachother. What happens when `(N - 1)` more polaroids are inserted between them ? Their axes are equally spaced. How does the transmitted intensity behave for large `N` ?

Explanation

Let `I_0` be the original intensity of unpolarised light,
Transmitted intensity through first polaroid is
`I_1 = I_0 cos^2 theta`
Similarly, transmitted intensity through second polaroid is
`I_2 = I_1 cos^2 theta = I_0 cos^2 theta cos^2 theta`
`= I_0 cos^4 theta`
If N polaroids are used, then
`I_N = I_0(cos theta)^(2N)`
The angle between successive polaroids is
`theta = (90^@)/N = (pi)/(2N) rad`
`:. (cos theta)^(2N) = (cos (pi)/(2N))^(2N)`
`= (1 - (pi^2)/(8 N2) + ......)^(2N)`
Using binomial theorem,
`(cos theta)^(2N) = (1 - (2Npi^2)/(8N^2) + ......)`
For large N, the above expression will approach 1.
`implies I_N = I_0`.