Concept:
Light exhibits several wave phenomena such as reflection, refraction, interference, diffraction, and polarisation. Among these, polarisation is the phenomenon that specifically proves that light waves are transverse in nature. In transverse waves, the particles of the medium vibrate perpendicular to the direction of propagation. Only transverse waves can be polarised because their vibrations occur in multiple possible directions perpendicular to the wave's direction of travel.
Step 1: Understanding polarisation. Polarisation is the phenomenon in which the vibrations of light waves are restricted to a single plane perpendicular to the direction of propagation. Normally, light waves vibrate in many different planes. When light passes through a polarising material, only vibrations in one particular plane are allowed to pass through.
Step 2: Relation to transverse waves. This restriction of vibrations is possible only if the wave has oscillations perpendicular to its direction of motion. Therefore, the existence of polarisation confirms that light behaves as a transverse wave. Longitudinal waves such as sound cannot exhibit polarisation because their oscillations occur parallel to the direction of propagation.
Step 3: Conclusion. Since only transverse waves can be polarised, the observation of polarisation in light proves that light is transverse in nature.