Which symmetry operator indicates a vertical mirror plane specifically aligned with the z-axis?

The vertical mirror plane, denoted as "sigmav," specifically refers to a plane that reflects points through it and is oriented vertically; in this context, it suggests alignment with the z-axis. This can be understood as follows:

In symmetry operations, a vertical mirror plane operates such that any point on one side of the plane will be reflected to an equivalent point on the opposite side, while the plane itself remains unchanged. Thus, when we talk about a vertical mirror plane aligned with the z-axis, we imply that the plane allows reflections along the vertical direction, maintaining the z-coordinate constant and changing only x and y coordinates.

In contrast, the other options represent different kinds of symmetry:

• A horizontal mirror plane, or "sigmah," reflects points across a horizontal plane (for example, one defined by a specific value of z), and does not provide reflections related to the vertical symmetry we see in "sigmav."

• "Sigmad" refers to a diagonal mirror plane that reflects through a plane at an angle rather than aligning purely vertically or horizontally.

• The identity operator "E" corresponds to no change at all, which does not apply to the idea of a reflection.

Therefore, "sigmav" is the