Answer:
1.[tex]\theta=29.84^{0}[/tex]
2.[tex]\theta=60.15^{0}[/tex]
Explanation:
Polarizes axis can create two possible angles with the vertical.
first we have to find the intensity of first polarizer
which is given as
[tex]I=\frac{I_{0} }{2}[/tex]
[tex]I= \frac{655\frac{W}{M^{2} } }{2}[/tex]
[tex]I=327.5\frac{W}{m^{2} }[/tex]
For a smaller angle for the first polarizer:
According to Malus Law
[tex]I_{2} =I_{1} Cos^{2}(90^{0} - \theta)[/tex]
[tex]I_{2} =I_{1} sin^{2}\theta[/tex]
[tex]\frac{I_{2} }{I_{1} }=Sin^{2}\theta[/tex]
taking square root on both sides
[tex]\sqrt{\frac{163}{327.5} } = sin\theta[/tex]
[tex]\theta=Sin^{-1}(0.4977)[/tex]
[tex]\theta=29.84^{0}[/tex]
For a larger angle for the first polarizer:
According to Malus Law
[tex]I_{2} =I_{1} cos^{2}\theta[/tex]
[tex]\frac{I_{2} }{I_{1} }=Cos^{2}\theta[/tex]
taking square root on both sides
[tex]\sqrt{\frac{163}{327.5} } = cos\theta[/tex]
[tex]\theta=Cos^{-1}(0.4977)[/tex]
[tex]\theta=60.15^{0}[/tex]
