1.7 Polarization (Page 3/20)

Page 3 / 20

This Open Source Physics animation helps you visualize the electric field vectors as light encounters a polarizing filter. You can rotate the filter—note that the angle displayed is in radians. You can also rotate the animation for 3D visualization.

Calculating intensity reduction by a polarizing filter

What angle is needed between the direction of polarized light and the axis of a polarizing filter to reduce its intensity by

90.0 %

Strategy

When the intensity is reduced by

90.0 %

, it is

10.0 %

or 0.100 times its original value. That is,

I = 0.100 I_{0} .

Using this information, the equation

I = I_{0} {cos}^{2} θ

can be used to solve for the needed angle.

Solution

Solving the equation

I = I_{0} {cos}^{2} θ

for

cos θ

and substituting with the relationship between I and

I_{0}

gives

cos θ = \sqrt{\frac{I}{I_{0}}} = \sqrt{\frac{0.100 I_{0}}{I_{0}}} = 0.3162 .

Solving for $θ$ yields

θ = {cos}^{−1} 0.3162 = 71.6 ° .

Significance

A fairly large angle between the direction of polarization and the filter axis is needed to reduce the intensity to

10.0 %

of its original value. This seems reasonable based on experimenting with polarizing films. It is interesting that at an angle of

45 °

, the intensity is reduced to

50 %

of its original value. Note that

71.6 °

18.4 °

from reducing the intensity to zero, and that at an angle of

18.4 °

, the intensity is reduced to

90.0 %

of its original value, giving evidence of symmetry.

Got questions? Get instant answers now!

Check Your Understanding Although we did not specify the direction in [link] , let’s say the polarizing filter was rotated clockwise by $71.6 °$ to reduce the light intensity by $90.0 %$ . What would be the intensity reduction if the polarizing filter were rotated counterclockwise by $71.6 °$ ?

also $90.0 %$

Got questions? Get instant answers now!

Polarization by reflection

By now, you can probably guess that polarizing sunglasses cut the glare in reflected light, because that light is polarized. You can check this for yourself by holding polarizing sunglasses in front of you and rotating them while looking at light reflected from water or glass. As you rotate the sunglasses, you will notice the light gets bright and dim, but not completely black. This implies the reflected light is partially polarized and cannot be completely blocked by a polarizing filter.

[link] illustrates what happens when unpolarized light is reflected from a surface. Vertically polarized light is preferentially refracted at the surface, so the reflected light is left more horizontally polarized. The reasons for this phenomenon are beyond the scope of this text, but a convenient mnemonic for remembering this is to imagine the polarization direction to be like an arrow. Vertical polarization is like an arrow perpendicular to the surface and is more likely to stick and not be reflected. Horizontal polarization is like an arrow bouncing on its side and is more likely to be reflected. Sunglasses with vertical axes thus block more reflected light than unpolarized light from other sources.

The figure is a diagram that shows a block of glass in air. The reflecting surface is horizontal. A ray labeled unpolarized light starts at the upper left and hits the center of the block, at an angle theta one to the vertical. Centered on this incident ray is are two double headed arrows, one horizontal and the other vertical. From the point where this ray hits the glass block, two rays emerge. One is the reflected ray that goes up and to the right at an angle of theta one to the vertical, and the second is a refracted ray that goes down and to the right at an angle of theta two to the vertical. The reflected light is labeled as partially polarized parallel to the surface. Two double headed arrows, similar to those on the incident ray, are shown centered on the reflected ray, but the vertical arrow is significantly shorter than the horizontal one. The refracted ray is labeled as partially polarized perpendicular to the surface. Two double headed arrows, similar to those on the incident ray, are shown centered on the reflected ray, but the horizontal arrow is significantly shorter than the vertical one. A note indicates that when theta one equals Brewster’s angle, the angle between the reflected and refracted ray is ninety degrees. — Polarization by reflection. Unpolarized light has equal amounts of vertical and horizontal polarization. After interaction with a surface, the vertical components are preferentially absorbed or refracted, leaving the reflected light more horizontally polarized. This is akin to arrows striking on their sides and bouncing off, whereas arrows striking on their tips go into the surface.

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Source: OpenStax, University physics volume 3. OpenStax CNX. Nov 04, 2016 Download for free at http://cnx.org/content/col12067/1.4

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