Why will an ideal polaroid filter transmit 50% of inciddent nonpolarized light?

Answer 1

Non polarized light has an essentially random orientation. Let's assume you are installing a horizontal polarizing filter. It will eliminate all vertical component of incoming light. Something at 45 degrees could be considered half vertical and half horizontal. The filter will allow the horizontal component to pass through while eliminating the vertical component. Similar calculations can be done for all other angles. As any angle will have a component of both horizontal and vertical, eliminating one will leave you with 50% of the original light.

Answer 2

Half the light arriving at a polaroid filter will be within the acceptance window, and converted to polarized light.

The other half of the light is at too great an angle to convert, so it is absorbed instead.

If you have three pieces of polarizing material, arrange two so that all light is blocked. Then put the third in between, The result will surprise you.

Try a clear plastic spoon or similar clear object, while watching, put stress on the object by bending it. This effect, called a polariscope is used to analyze structural designs, it also is used to measure the purity of sugar.