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` ?
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When `(N - 1)` polaroids are inserted between two polaroids total number of polaroids `=(N + 1)`. The axes of all polaroids are equally spaced. If `theta` is the angle between the axes of any two consective polaroids, then `theta + theta + theta + .......N times = 90^(@) = pi//2` `N theta = pi//2` `theta = pi//2 N`. According to Law of Malus, intensity of light passing through a given pair of polaroids is proportinal to `cos^(2) theta`.In the given case, this change is repeated `N` times. If `I_(0)` is intensity of incident light and `I` is intensity of light coming out of last polaroid, then `I = I_(0) (cos^(2) theta)^(N) = I_(0) (cos theta)^(2N)` `= I_(0) "cos"((pi)/(2 N))^(2 N)` When `N` is very large, `theta = (pi)/(2N)` approaches zero and `cos (pi//2 N)` approaches `1`. Hence when `N` is very large, I will approach `I_(0)`.
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