Question
Two polaroids $${P_1}$$ and $${P_2}$$ are placed with their axis perpendicular to each other. Unpolarised light $${I_0}$$ is incident on $${P_1}.$$ A third polaroid $${P_3}$$ is kept in between $${P_1}$$ and $${P_2}$$ such that its axis makes an angle $${45^ \circ }$$ with that of $${P_1}.$$ The intensity of transmitted light through $${P_2}$$ is
A.
$$\frac{{{I_0}}}{2}$$
B.
$$\frac{{{I_0}}}{4}$$
C.
$$\frac{{{I_0}}}{8}$$
D.
$$\frac{{{I_0}}}{{16}}$$
Answer :
$$\frac{{{I_0}}}{8}$$
Solution :
According to the question
From the above diagram, intensity transmitted through $${P_3}$$
$$\eqalign{ & {I_2} = \frac{{{I_0}}}{2}{\cos ^2}{45^ \circ } \Rightarrow {I_2} = \frac{{{I_0}}}{2} \times {\left( {\frac{1}{{\sqrt 2 }}} \right)^2} \cr & \Rightarrow {I_2} = \frac{{{I_0}}}{4} \cr} $$
Similarly, intensity transmitted through $${P_2},$$
$$\eqalign{ & {I_3} = \frac{{{I_0}}}{4}{\cos ^2}{45^ \circ } \Rightarrow {I_3} = \frac{{{I_0}}}{4} \times {\left( {\frac{1}{{\sqrt 2 }}} \right)^2} \cr & \Rightarrow {I_3} = \frac{{{I_0}}}{4} \times \frac{1}{2} \Rightarrow {I_3} = \frac{{{I_0}}}{8} \cr} $$
According to the question
From the above diagram, intensity transmitted through $${P_3}$$
$$\eqalign{ & {I_2} = \frac{{{I_0}}}{2}{\cos ^2}{45^ \circ } \Rightarrow {I_2} = \frac{{{I_0}}}{2} \times {\left( {\frac{1}{{\sqrt 2 }}} \right)^2} \cr & \Rightarrow {I_2} = \frac{{{I_0}}}{4} \cr} $$
Similarly, intensity transmitted through $${P_2},$$
$$\eqalign{ & {I_3} = \frac{{{I_0}}}{4}{\cos ^2}{45^ \circ } \Rightarrow {I_3} = \frac{{{I_0}}}{4} \times {\left( {\frac{1}{{\sqrt 2 }}} \right)^2} \cr & \Rightarrow {I_3} = \frac{{{I_0}}}{4} \times \frac{1}{2} \Rightarrow {I_3} = \frac{{{I_0}}}{8} \cr} $$
