A) \[\cos \theta ={{\left( \frac{2}{3} \right)}^{1/4}}\]
B) \[\cos \theta ={{\left( \frac{1}{3} \right)}^{1/4}}\]
C) \[\cos \theta ={{\left( \frac{1}{3} \right)}^{1/2}}\]
D) \[\cos \theta ={{\left( \frac{2}{3} \right)}^{1/2}}\]
Correct Answer: A
Solution :
Let initial intensity be I. intensity of the beam after passing through A is\[{{I}_{1}}=\frac{I}{2}\] given that intensity after B is \[\frac{I}{2}.\]then angle between A and B is zero. A polariser C is introduced between A and C then by Molus law after B \[{{I}_{b}}=\frac{I}{2}{{\cos }^{2}}\theta \] and after\[C\,{{I}_{c}}={{I}_{b}}{{\cos }^{2}}\theta \] so given \[{{I}_{c}}=\frac{I}{3}\] from here solving all the three equations\[\frac{I}{3}=\frac{I}{2}{{\cos }^{4}}\theta \] \[\cos \theta ={{(\frac{2}{3})}^{\frac{1}{4}}}\]
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