Wave Optics Theory of Light

The behavior of light is explained by a combination of Ray Theory and Wave Theory. Historically, light was studied as rays; progress in electromagnetic theory led to the understanding of light as an electromagnetic radiation and wave theory of light. This article takes a basic look at the principles of wave theory in optics.

When Wave Theory Applies

When light interacts with objects larger than the wavelength of the light, the ray model tends to be a more suitable model to apply. For small-sized objects and apertures (usually, where the size of the objects and the wavelength of length are comparable), the wave theory comes into play.

Huygen's Principle

Huygen's Principle is a method of understanding wave propagation. At any moment in time it breaks the wavefront up into a series of points. From each of these points originates a circular ripple. These ripples all combine to produce a wavefront that propagates through the transmission medium. ‘Every point in a wavefront is a source of wavelets.’ This is demonstrated in Figure 1.

Figure 1. Huygens' Principle.

According to Huygen’s principle, the new wave-front is the tangential surface to all of these secondary wavelets. This principle explains reflection, refraction, diffraction and interference of light.

Diffraction and Huygen's Principle

As Huygen's principle is based on geometry, as long as the wavelength and any interfering objects are scaled up at the same rate, the wave behavior remains unchanged. For this reason, the Huygen's principle can equally explain the passage of light through a tiny slit in a barrier or the passage of an ocean wave through an aperture in a breakwall.

In order to calculate the angular features of the diffraction pattern, we need the ratio λ/d where d refers to the size of a feature in the diffracting object.

Because the light wave follows Huygen’s principle, light does not form a perfect image of the slit, but diffracts to form a ‘spread out’ image of the aperture. The aperture is the new wave source.

Double Slit Diffraction

When applying Huygen's principle to double slit diffraction, two sets of ripples originating at each slit need to be constructed. The angles corresponding to the bright points (maxima) and dark points (minima) area given by the equation:

Where d is the slit spacing and m is an integer corresponding to one of the maxima or an integer and a half for a minima.

Diffraction Grating

If a double slit pattern is repeated hundreds or thousands of times, we get a diffraction grating. The diffraction fringes remain in the same places, but become much narrower. Depending on the size of the grating and the wavelength of the light, the diffraction grating acts as a dispersive element, resulting in a structural coloration - the light split and diffracted into several beams propagating in different directions.

This article was updated on 14^th June, 2019.