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Unpolarized light falls on two polarizin...

Unpolarized light falls on two polarizing sheets placed one on top of the other. What must be the angle between the characteristic directions of the sheets if the intensity of the final transmitted light is one - third the maximum intensity of the first transmitted beam

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Intensity of the light transmitted through the first polarizer `I_(1)= I_(0)"/"2`, where `I_0` is the intensity of the incident unpolarized light.
Intensity of the light transmitted through the second polarizer is `I_(2)= I_(1) cos^(2) theta" where "theta` is the angle between the characteristic directions of the polarizer sheets.
But `I_(2)= I_(0)"/"3` (given) `" "therefore I_(2)= I_(1)cos^(2)theta= (I_0)/(2)cos^(2) theta= (I_0)/(3)`
`cos^(2) theta = 2"/"3 implies theta = cos^(-1) sqrt((2)/(3))`.
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