Answer:
51.94°
Explanation:
[tex]I_0[/tex] = Unpolarized light
[tex]I_2[/tex] = Light after passing though second filter = [tex]0.19I_0[/tex]
Polarized light passing through first filter
[tex]I_1=\frac{I_0}{2}[/tex]
Polarized light passing through second filter
[tex]I_2=\frac{I_0}{2}cos^2\theta\\\Rightarrow 0.19I_0=\frac{I_0}{2}cos^2\theta\\\Rightarrow cos^2\theta=\frac{0.19I_0}{\frac{I_0}{2}}\\\Rightarrow cos\theta=\sqrt{\frac{0.19I_0}{\frac{I_0}{2}}}\\\Rightarrow \theta=cos^{-1}\sqrt{\frac{0.19I_0}{\frac{I_0}{2}}}\\\Rightarrow \theta=cos^{-1}\sqrt{0.19\times 2}\\\Rightarrow \theta=cos^{-1}\sqrt{0.38}\\\Rightarrow \theta=51.94^{\circ}[/tex]
The angle between the two filters is 51.94°
