The light coming from a Nicol prism shows no variation in intensity

a) The emergent light can be unpolarized
The emergent light from a Nicol prism can be unpolarized because a Nicol prism is a type of polarizing prism that is designed to transmit only light waves that are polarized along a specific axis. However, if the incident light is not polarized or is polarized in a different direction than the prism's axis, the emergent light will be unpolarized. In this case, the emergent light will have no specific direction of polarization and will show no variation in intensity.

b) The emergent light can be circularly polarized
Circularly polarized light is a type of polarized light in which the electric field vector rotates in a circular motion as the light propagates. While a Nicol prism is designed to transmit linearly polarized light, it is possible for the emergent light to be circularly polarized if the incident light is already circularly polarized. In this case, the Nicol prism will not affect the polarization state of the light, and the emergent light will also be circularly polarized.

c) The emergent light can be plane polarized
Plane polarized light is a type of polarized light in which the electric field vector oscillates in a single plane as the light propagates. A Nicol prism is specifically designed to polarize light and transmit only one specific plane of polarization. Therefore, the emergent light from a Nicol prism can be plane polarized if the incident light is already polarized in the same direction as the prism's axis. In this case, the Nicol prism will transmit the light without any change in its polarization state, and the emergent light will also be plane polarized.

d) The emergent light can be elliptically polarized
Elliptically polarized light is a type of polarized light in which the electric field vector traces an ellipse as the light propagates. A Nicol prism is not designed to produce or transmit elliptically polarized light. Therefore, if the incident light is elliptically polarized, the Nicol prism will alter its polarization state and the emergent light will no longer be elliptically polarized. Thus, the emergent light from a Nicol prism cannot be elliptically polarized.

In summary, the emergent light from a Nicol prism can be unpolarized or circularly polarized, but not plane polarized or elliptically polarized.