**Distinguishing Elliptically Polarized Light (EPL) from a Mixture of Plane Polarized (PPL) and Unpolarized Light (UPL)**

To distinguish between elliptically polarized light (EPL) and a mixture of plane polarized (PPL) and unpolarized light (UPL), we can utilize a few key characteristics of these types of light.

1. **Intensity Variation**: One way to distinguish EPL from a mixture of PPL and UPL is by examining the intensity variation of the light. EPL exhibits a regular and periodic variation in intensity as the electric field vector rotates. On the other hand, a mixture of PPL and UPL will not exhibit such a regular intensity variation.

2. **Angular Distribution**: EPL typically has a specific angular distribution of intensity, which can be observed by using a polarization analyzer. By rotating the analyzer, we can detect a change in intensity as the analyzer aligns with the direction of the elliptical polarization. In the case of a mixture of PPL and UPL, the angular distribution will not exhibit a clear pattern.

3. **Phase Shift**: EPL shows a phase shift between the orthogonal components of the electric field vector. This phase shift can be detected by using a quarter-wave plate, which introduces a specific phase difference between the two orthogonal components. If the light is EPL, the output intensity will vary as the plate is rotated. In the case of a mixture of PPL and UPL, the phase shift will not be present, and the output intensity will not vary with the rotation of the plate.

4. **Polarization Ellipse**: EPL can be characterized by an elliptical polarization ellipse. By using a polarization analyzer, we can observe the shape and orientation of the polarization ellipse. If the light is a mixture of PPL and UPL, the polarization ellipse will not be clearly defined and may appear as a circle or an irregular shape.

**Distinguishing Circularly Polarized Light (CPL) from Unpolarized Light (UPL)**

To distinguish circularly polarized light (CPL) from unpolarized light (UPL), we can employ the following methods:

1. **Circular Dichroism**: CPL exhibits circular dichroism, which means that it selectively absorbs left-handed circularly polarized light or right-handed circularly polarized light. By passing the light through a circular polarizer, we can determine if there is a change in intensity. If the intensity changes, it indicates the presence of CPL. UPL, on the other hand, will not exhibit any significant change in intensity.

2. **Polarization Analyzer**: Using a polarization analyzer, CPL can be distinguished from UPL by observing the intensity variation as the analyzer is rotated. CPL will exhibit a regular and periodic variation in intensity, whereas UPL will not show any distinct pattern.

3. **Interference Patterns**: CPL can produce interference patterns when interacting with a suitable medium, such as a birefringent material. These interference patterns will have characteristic features specific to circular polarization. UPL will not produce such interference patterns.

4. **Phase Shift**: CPL shows a phase shift of 90 degrees between the two orthogonal components of the electric field vector. This phase shift can be detected using a quarter-wave plate, which introduces a fixed phase difference. If the light is CPL, the output intensity will vary as the plate is rotated