Plane Polarized Light

[MedPR]

TBR Example 10.2b

When unpolarized light reflects off a specular (mirrored) surface at a glancing angle with respect to the surface, the light can partially polarize parallel to the surface. That is, the parallel polarized light is more intense than the perpendicular polarized light. If this surface is lying onflat ground, in what orientation should a polarizing anti-glare filter be with respect to the ground, in order to minimize the total light intensity through the filter? The polarizer's polarization axis should be oriented at:

C. 90deg relative to the ground.

Intuitively I understand this, but in a previous example TBR mentioned Malus' law as the equation to use when calculating the amount of linearly polarized light gettin through a polarizer.

The equation is I=Iocos^2theta. I is the final intensity (intensity getting through the polarizer), Io is the initial intensity of the light, and theta is the angle between the light's polarization direction and the polarization axis of the polarizer.

I tried to use that equation to answer the question, but couldn't figure out how if I/Io should be 0, or if it should be 1. If you want to reduce the intensity of the polarized light, should I/Io be 1? Or should it be 0? Also, how do you solve cos^2theta = x problems?

For example, cos90 is 0 (hence why I figured I/Io should be 0, since you want your polarizer to be 90deg relative to the ground), but how do you do the sqrt of 0? How would you solve cos^2theta=0?

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[milski]

Io is the intensity before going through the filter, I after. You want to decrease glare, thus you want the minimal I. The minimum of cosθ^2 is 0, that's when cosθ is 0, that's when θ is π/2.

sqrt(0) is 0, that's easy to verify by squaring both side - sqrt(0)*sqrt(0)=0*0=0

 

[ilovemedi]

Does anyone understan Malus's law? In I=Iocos(theta)^2, what is THETA? I tried looking up images, but am still confused.

On the same note, any SDN-ers understand example 10.2a on TBR light/optics chapter??

 

[milski]

θ is the angle between the plane in which the light is polarized and the plane in which the filter polarizes light.

This formula is applicable only for already polarized light. It's easy to consider the two extremes: If the filter is aligned with the plane of polarization, the angle is 0, cos θ is 1 and the intensity is the same as Io. That makes sense, since the filter is not doing anything to the light - it's polarizing in the same direction it already was polarized, so all of the light passes through.

In the case where the angle between them is pi/2, cos θ is 0 and none of the light passes. That again makes sense, since none of the polarized light can pass through the filter.