Two polaroids have their polarizing directions parallel so that the intensity of a transmitted light is maximum. The angle through which either polaroid must be turned if the intensity is to drop by one-half is
A.
$${135^ \circ }$$
B.
$${90^ \circ }$$
C.
$${120^ \circ }$$
D.
$${180^ \circ }$$
Answer :
$${135^ \circ }$$
Solution :
$$\eqalign{
& {\text{For}}\,\,I = \frac{{{I_0}}}{2}\,\,{\text{and}}\,\,I = {I_0}{\cos ^2}\theta = \frac{{{I_0}}}{2} \cr
& \therefore \theta = {45^ \circ } \cr} $$
Therefore the angle through which either polaroids turned is $${135^ \circ }\left( { = {{180}^ \circ } - {{45}^ \circ }} \right)$$
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