The fact that light WAVES are transverseand not longitudinal is demonstrated by the phenomenon of polarization.
A beam of light has waves which RADIATE in all directions.
A polarizing filter acts as though it has tiny slits which are either vertical or horizontal. When light enters a POLARIZING filter, only some waves can pass through.
The light which passes through is called POLARIZED light.
http://www.colorado.edu/physics/2000/polarization/polarizationI.html Polarized light Unpolarized light
If you place one POLARIZING filter on top of another and rotate one of them, you will see how the amount of light coming through changes. Link