A) \[45{}^\circ \]
B) \[90{}^\circ \]
C) \[30{}^\circ \]
D) \[60{}^\circ \]
Correct Answer: A
Solution :
(i) The value of\[\theta \] is\[90{}^\circ \]for which the intensity of emergent light from\[{{P}_{2}}\]is zero as \[cos\text{ }90{}^\circ =0\] (ii) If\[{{I}_{0}}\]be the intensity of uhpolarised light on \[{{p}_{1}},\]then the intensity of light emerging from \[{{p}_{1}}\]will be \[\frac{{{I}_{0}}}{2}\]. The intensity of light after passing through second test polaroid\[{{p}_{2}}\]will be \[I=\frac{{{I}_{0}}}{2}{{\cos }^{2}}\theta {{\sin }^{2}}\theta \] So, \[\frac{{{I}_{0}}}{8}=\frac{{{I}_{0}}}{8}{{\sin }^{2}}2\theta \] \[{{\sin }^{2}}2\theta =1\] \[\sin 2\theta =1\] \[2\theta =90{}^\circ \] \[\theta =45{}^\circ \]
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