Why when I use a polarized lens if I turn it one way the rainbow disappears and the other way it brings it out better to the point you can see the second double rainbow when the naked eye can't?
Is there a drawing for this?
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The obvious answer is that the light from a rainbow, or at least the portion that is fitting in your viewfinder at the time you are rotating the polarizer, is all polarized in the same direction.¹ That is, the light reflecting off of millions of water droplets falling in the atmosphere is polarized in the same way by the more or less uniform shape of those droplets as they fall.
That explains how it can be blocked, but how is it enhanced by the lens?
When you rotate a polarizer you are changing the direction of the polarized light that is filtered out. What is left is easier to see since the competing light polarized in a different direction is no longer making it through the filter.
It's not really enhanced, as in 'increased', by the filter. But when competing light polarized in a different direction is eliminated, what is left is easier to see. It's the same way polarized sunglasses work. By filtering out bright glare, one can see details that were already present, but being drowned out by the glare.
¹ As scottbb points out in a comment, if an entire rainbow from horizon to horizon is wide enough, and the lens' field of view is wide enough to see all of it at once, the polarizer won't affect the entire rainbow equally for any single position of the polarizer.
Light travels in a wave much like water waves seen on the surface of a pond. Water waves undulate in an up – down direction whereas light waves vibrate up – down, left – right, and diagonally. As a matter of fact light waves undulate in all possible planes. This is true for light waves arriving from sun. In other words, light from the sun is not polarized. Light becomes polarized when light traverses certain transparent liquids and when light is reflected from certain reflective surfaces. What happens is: light normally undulating in all possible planes, encounters objects that change or limit the direction of the wave vibration.
OK light waves from the sun are not polarized, they pass through the earth’s atmosphere which might be saturated with water vapor or supporting haze, smoke, or dust. When the vibration direction of the waves are altered, we call this polarization. The word comes from the fact that early on, scientist believed light rays has a positive and a negative component like the poles of a magnet. Thus when they saw changes in direction of oscillation they called it polarization. This turned out to be a false assumption.
Now the polarizing filter has imbedded in it, transparent mineral crystals that block light that vibrates in all planes but one. As you rotate the filter, the orientation plane of the light waves that can get through the filter change. The rainbow is caused when light traverses water droplets suspended in the air. These droplets change the direction of travel of the light waves (refraction – to bend inward), plus they polarize the light wave.
As you rotate the polarizing filter, at some positions, light from rainbow in blocked and in some positions light traverses the filter. In some positions the sky behind the rainbow is darkened and in some positions the contrast between sky and rainbow are reduced. This all come under the heading of color as seen and photographed. There are lots of books on this subject.