# What determines the colour of viewed light that has been linearly then circularly polarised and viewed through a linear polarising filter?

I have run a little science experiment using a white light table with a linear polarising filter atop it and gotten students to stick sellotape on acetate to act as a circular polariser so that when viewed through 3D glasses (linear polarisers) it reveals different colours based on the angle and rotation from which they are viewed as well as layering of the sellotape. Pretty much as shown at the beginning of this video.

I have a relatively good grasp of scientific concepts; my current understanding is that elliptical/circular polarisation occurs when light is refracted through an anisotropic medium, which in this case is the sellotape (and acetate to some extent) and this slows down one component of the EM waves.

But what is it that determines the colour you see when you view the circularly polarised light through another linear polarising filter (3D glasses)?

Thank you.

• polarizer may increase color saturation , decrease reflections, then filter or relatively highlight some colors tones.
– user46925
Aug 3, 2016 at 21:44
• The spectrum of the light. Aug 3, 2016 at 22:14
• @igael This is true with regards to photography and that is because the light reflected off of water and other such surfaces often has a degree of polarisation due to its interaction with light. The CPL has a quarter wave plate relation-ship with the linear polariser and can be used to filter out the reflected light by turning the linear polarising filter component to negate the reflected light. Aug 4, 2016 at 7:01
• @CuriousOne The spectrum of light i.e. white light certainly contains a wide range of wavelengths which accounts for all the different colours. What I am trying to understand is how only a specific wavelength of colour is observed based on the material and viewing conditions through the linear polarising filter on the 3D glasses Aug 4, 2016 at 7:04
• Polarization has nothing to do with the spectrum of the light, it's an independent quantity. Good 3d glasses will not discolor the light passing trough them. The cheap ones you get in the theatre most likely will, but that's a technical defect and not some fundamental property of light. Aug 4, 2016 at 7:09

Simplified, it's interference patterns across different wavelengths based on the thickness of the material.

If you used monochromatic light, you would likely see an interference pattern that was related to the thickness of the material. The index of refraction differs based on the polarization orientation. At some thicknesses the phase of each will match on exit (same as if it had a uniform index of refraction) and at other thicknesses the two directions will be out of phase.

But because the indices of refraction differ with wavelength, the thickness that allows red light to be seen through the polarizers may not allow green light to be seen through them.

Using some optical filters should show a much simpler pattern on the materials.

so it is simpler to see this as a problem of diffraction as the chains of hydrocarbons in the sellotape will act as a diffraction grid and depending on the angle of viewing I will get either a constructive or destructive fringe

The interference isn't from the chains directly. Instead the chains change the index of refraction based on the orientation of the light's electric field. This turns the piece into a waveplate.

Different thicknesses mean it might act like a half-wave plate for some wavelengths (reversing the direction of the circular polarization and allowing the light to be visible), and it might act like a full-wave plate for others (leaving it alone for the second filter to absorb the wave.

• Thank you for your reply. I see, so it is simpler to see this as a problem of diffraction as the chains of hydrocarbons in the sellotape will act as a diffraction grid and depending on the angle of viewing I will get either a constructive or destructive fringe which may or may not coincide with that of another wavelength (thus mixing and giving another colour)? Aug 4, 2016 at 7:10
• Again thank you for your added answer, I accept your response as the answer but I would appreciate if you could elucidate a little further the last bit of the question which is, why can the interference caused by the sellotape (whether to monochromatic light or white light) only be observed once viewed through another linear polariser and not the naked eye? Aug 4, 2016 at 9:12
• Most of the light goes through the test material, just some of the polarization properties have changed. Your eye cannot see this change in polarization and views it as nearly uniform. The second polarizer removes the light that has not been phase modifed, leaving only the sections where such changes happened. This subtraction by the second filter allows you to see the modified areas. Aug 4, 2016 at 15:43