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Question

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


A
15o
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B
35o
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C
55o
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D
75o
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Solution

The correct option is A $${ 55 }^{ o }$$
Intensity of unpolarized light $$I'=\cfrac { I }{ 2 } \cos ^{ 2 }{ \theta  } $$
$$\therefore \cfrac { I }{ 2 } \cos ^{ 2 }{ \theta  } =\cfrac { I }{ 6 } $$
$$\Rightarrow \cos ^{ 2 }{ \theta  } =\cfrac { 1 }{ 3 } $$
$$\Rightarrow \cos { \theta  } =\cfrac { 1 }{ \sqrt { 3 }  } $$
$$\therefore \theta ={ 55 }^{ o }$$

Physics

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