The angle of incidence, when there is perfect transmission is the polarization angle. The expression for the polarization is
[tex]\theta = 90-\phi[/tex]
Where
[tex]\theta[/tex] = Polarization angle
[tex]\phi[/tex] = Angle with the vertical axis
We have that the angle is
[tex]\theta = 90-19.5[/tex]
[tex]\theta = 70.5\°[/tex]
The ratio of the intensities depends on the cosine of the polarization angle. The polarization angle found from the wearer’s leaning angle can be used to find the fraction of the reflected ray intensity that will pass through the sunglasses.
Applying the Malus Law we have that
[tex]\frac{I}{I_0} = cos^2 \theta[/tex]
Here,
[tex]I[/tex] = Final intensity
[tex]I_0[/tex] = Initial intensity
Replacing we have,
[tex]\frac{I}{I_0} = cos^2 (70.5)[/tex]
[tex]\frac{I}{I_0} = 0.11[/tex]
Therefore the fraction of the reflected light intensity which passes through the sunglasses is 0.11
