To develop this problem it is necessary to apply the concepts related to the law of Malus.
Malus's law defines that,
[tex]I = I_0 cos^2\theta[/tex]
Where
[tex]I_0 =[/tex] Intensity of incident light
I = Intensity of polarized light
Therefore according to the information
[tex]I = I_0 \frac{15}{100}[/tex]
[tex]I = 0.15I_0[/tex]
Equation we have that
[tex]0.15 I_0 = I_0 \frac{15}{100}[/tex]
[tex]cos^2\theta = 0.15[/tex]
[tex]cos\theta = 0.3872[/tex]
[tex]\theta = cos^{-1}(0.3872)[/tex]
[tex]\theta = 67.2\°[/tex]
Therefore the angle the polarization of the light make with the horizontal after passing through the polarizer is 67.2°
