A) If passing light through two crossed polarizers with transmission axes 90 deg

Question

A) If passing light through two crossed polarizers with transmission axes 90 degrees apart results in no light getting through, and sticking a third polarizer in the middle at 45 degrees suddenly makes some light appear coming out the end of the arrangement, how do you explain that? Hint: if your answer contains the word “rotate/rotation”, think again!

B) Explain in your own words how linearly polarized light might be interpreted as the sum of equal amounts of right- and left-handed circularly polarized light.

Please explain part A and part B EACH in a LENGTHY WORD PARAGRAPH supported by equation (if necessary).

Explanation / Answer

A) A single polarizer allows only the component of light’s electric vector that is parallel to it's axis unattenuated. Light whose electric vector is perpendicular to it's axis cannot pass through at all. Light whose electric vector points in any other direction passes through according to the magnitude of the component that is parallel to the axis. The polarizer thus blocks half the incident light, and the transmitted light is polarized in the direction of the axis of the polarizer.

When a second polarizer placed in front of the first one with it's axis perpendicular to that of the first polarizer and thus also perpendicular to the electric vector of the emerging light, it blocks all of this light, and none of the light will pass through the polarizer.

When a third polarizer is placed between the other two with it's axis at 45 degrees to theirs. Some of the light that was blocked now gets through to the screen. The electric vector of the light coming from the first polarizer has a component that is parallel to the easy axis of the middle polarizer, so some of the light can pass through. The emerging light is now polarized at 45 degrees to its original direction and also to the axis of the next polarizer. The electric vector thus has a component that is parallel to this polarizer’s easy axis, and again some of it can pass through, illuminating the circular area on the screen. With all three polarizers in place, at each polarizer half the incident light is transmitted, so one-eighth of the light reaches the screen.

B) When the two perpendicular polarized electric field are added, they form diagonal or anti-diagonal polarized light. To generate circularly polarized light, the two electric field should be out of phase. When the phase shift is exactly ±90°, then circular polarization is produced. Thus circular polarization is created starting with linearly polarized light and employing a quarter-wave plate to introduce such a phase shift. Note that circular olarization can involve either a clockwise or counterclockwise rotation of the field. These correspond to distinct polarization states.

The current situation can be understood in the process reverse to what explained in the previous paragraph. When circularly polarized light can be explained in terms of the equal amounts of two orthogonal linear polarized light and one of them lag/lead with other. In the similar way, by adding equal amounts or right- and left-handed circularly polarized light, linearly polarized can be generated. A quarter wave plate can be used to perform this operation.

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