Wave optics: wavefront and Huygens’ principle

Introduction

The link between waves and light rays is the subject of wave optics, also known as physical optics. When the wave qualities of light are taken into account, it is utilized. It is concerned with the study of diverse phenomena such as polarization, diffraction, interference, and other occurrences when geometric optics cannot be represented by rays. 

The branch of optics that deals with the behavior of light and its wave characteristics is known as wave optics. When studying and analyzing waves, Huygens principle is one of the most significant principles to remember. Huygens concept essentially aids us in comprehending and describing wave motion.

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Wave Optics Theories

According to Sir Isaac Newton’s corpuscular theory, “Light is made up of incredibly small tiny particles called corpuscles that travel at extremely high speeds from the source of light to create a visual sensation by reflecting on the retina of the eyes.”The main flaw in Newton’s corpuscular theory was that it failed to explain why the velocity of light in denser media was lower than in vacuum.

Until Christopher Huygens introduced his wave theory of light in the early 18th century, no one dared to dispute Newton’s corpuscular hypothesis. Light, according to Huygens hypothesis, light is made up of waves that travel through a dilute and highly elastic medium that exists everywhere in space.” This medium is ether.

Huygens Wave Theory

Huygen proposed the wave theory. He claimed that light travels in the form of waves. His theory states that “Every point on a wavefront is in itself the source of spherical wavelets, which spread out in the forward direction at the speed of light. The sum of these spherical wavelets forms the wavefront.”

In the same medium, these secondary wavelets propagate at the speed of light. A wavefront is a real or imaginary surface on which the oscillation phase is constant.

This explanation however, does not explain why refraction happened in the first place. 

Second, it couldn’t tell us how light transfers energy along its path.

Secondary Wavelet Principle of Huygens – Statement

Huygens principle, commonly known as the Huygens–Fresnel principle, asserts that each point on a wavefront will generate secondary wavelets or disturbances. Furthermore, disturbances caused by the secondary source spread in all directions the same way as those caused by the primary source do. The principle also says that

• Secondary sources begin to produce their own wavelets, which are identical to those produced by the primary source. 
• At any given time, the common tangent on the wavelets in the forward direction produces a new wavefront. 
• The wavefront is formed by the sum of spherical wavelets.

Refraction of the plane wave using Huygens Principle

Consider a plane wavefront AB that is incident on the surface, as indicated in the diagram below. Let v1 and v2 be the incident and refracted ray velocities of medium 1 and 2, respectively (v1>v2). The waves’ velocity is determined by the medium. The source of secondary spherical wavelets comes from Huygens principle A and C. Let t be the time it takes to get from B to C.

As a result, BC = v1t in medium 1

Draw a sphere of radius v2t from point A in the second medium to calculate the shape of the refracted wavefront. At time t, it represents the secondary spherical wavefront.

In medium 2, AD = v2t.

The tangent formed from point C to the sphere is now CD. The refracted wavefronts are thus AD and CD.