Answer:
The angle between the transmission axes of the filters is 65°
Explanation:
The complete question is
Unpolarized light is incident upon two ideal polarizing filters that do not have their transmission axes aligned. If 18% of the light passes through this combination, what is the angle between the transmission axes of the two filters.
From Malus law,
[tex]I = I_{0} cos^{2} \beta[/tex] ....1
where [tex]I[/tex] is the intensity of the polarized light,
[tex]I_{o}[/tex] is the intensity of the incident light
β the angle between the transmission axes of the two filters
Since the intensity is reduced to 18% or 0.18 of its initial value, this means that
[tex]cos^{2} \beta[/tex] = 0.18
substituting into the equation above, we have
[tex]I = 0.18I_{0}[/tex] ....2
equating the two equations, we have
[tex]I_{0}cos^{2} \beta[/tex] = [tex]0.18I_{0}[/tex]
[tex]cos^{2}\beta[/tex] = [tex]\frac{0.81I_{0} }{I_{0} }[/tex] = 0.18
[tex]cos \beta[/tex] = [tex]\sqrt{0.18}[/tex] = 0.424
[tex]\beta[/tex] = [tex]cos^{-1} 0.424[/tex] = 64.9 ≅ 65°
