How can you determine the direction of the polarizing axis of a single polarizer?

The law states that the intensity of a beam of plane-polarized light after passing through a rotatable polarizer varies as the square of the cosine of the angle through which the polarizer is rotated from the position that gives maximum intensity.

The shine of horizontal table comes from the horizontally polarized light that is refracted. If one look at the table through the polarizer and turn it around at a certain position, the table will be mostly shiny and at certain position will be most dull. The dull position means that the polarizing axis is perpendicular to the table and the shiny one means that the polarizing axis is parallel with the table.

Hence, one can determine the direction of the polarizing axis of a single polarizer.