A mixture of plane polarised and unpolarised | vedclass

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Question

(A) Let $I_P$ be the intensity of the plane polarized light and $I_0$ be the intensity of the unpolarized light.When the light passes through a polari

Vedclass · Accepted Answer

$3/2$

Vedclass · Answer

(A) Let $I_P$ be the intensity of the plane polarized light and $I_0$ be the intensity of the unpolarized light.When the light passes through a polarizer,the transmitted intensity of the polarized component is $I_P \cos^2 	heta$ and the unpolarized component is $I_0/2$.The total transmitted intensity is $I = I_P \cos^2 	heta + I_0/2$.The maximum intensity occurs at $	heta = 0^{\circ}$,so $I_{\max} = I_P + I_0/2$.The minimum intensity occurs at $	heta = 90^{\circ}$,so $I_{\min} = I_0/2$.Given that the intensity varies by a factor of $4$,we have $I_{\max} = 4 I_{\min}$.Substituting the expressions: $I_P + I_0/2 = 4(I_0/2) = 2I_0$.Rearranging gives $I_P = 2I_0 - I_0/2 = 3I_0/2$.Therefore,the ratio $I_P/I_0 = 3/2$.

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