Polarization by reflection and Brewsters Angle

[Sswift]

Homework Statement

A beam of light is reflected off the surface of some unknown liquid, and the light is examined with a linear sheet polarizer. It is found that when the central axis of the polarizer (that is, perpendicular to the plane of the sheet) is tilted down from the vertical at an angle of 54.3 Degrees,the reflected light is completely passed provided the transmission axis is parallel to the plane of interface. From this information, compute the index of refraction of the liquid.

Homework Equations

tan θ_p=n_t/n_i
n_i≈1

The Attempt at a Solution

So I think that the since the light is completely passed through the polarizer that my angle θ_p is just the 54.3 degrees that the polarizer is tilted at, but when I draw up what I believe to be happening I think that brewsters angle which is also the angle of reflection is 35.7 degrees rather than 54.3. But if I was to plug this into the equation above and solve for n_t I get a value less than one. Using 54.3 degrees gives me an answer that makes sense. I'm just not sure why I use that angle, any help?

 

[TSny]

So I think that the since the light is completely passed through the polarizer that my angle θ_p is just the 54.3 degrees that the polarizer is tilted at, but when I draw up what I believe to be happening I think that brewsters angle which is also the angle of reflection is 35.7 degrees rather than 54.3.

Why do you think the Brewster angle is 35.7 degrees rather than 54.3 degrees?