Wave optics, also known as Physical Optics, is the study of phenomena such as polarization, diffraction, interference and other occurrences where the ray approximation of geometric optics cannot be applied. This section of optics deals with the behaviour of light and its wave characteristics.

In wave optics, we will learn about the concept of using ray optics for the estimation of the field on a surface, and integrating the ray-estimated field over a mirror, lens or aperture for the calculation of the scattered or transmitted field in detail for IIT JEE here.

Table of Contents

Wave Optics Theories

Huygens Wave Theory

Maxwell’s Electromagnetic Theory

Wavefront and Wave Normal

Coherent and Incoherent Sources

Wave Optics Theories

Wave optics serves as a testament to the famous dispute between two great scientific communities who devoted their lives to comprehending the essence of light. One group advocated for the particle nature of light, while the other championed the wave nature.

Sir Isaac Newton is a renowned figure that advocated for the particle nature of light, proposing a corpuscular theory which states that “light is composed of extremely small and lightweight particles known as corpuscles that travel at very high speeds from the source of light to produce a sensation of vision when reflected on the retina of the eye”.

Check Out: Young’s Double Slit Experiment

The major failure of Newton’s corpuscular theory was that it could not explain the cause of interference, diffraction, polarization, and why the velocity of light was lesser in a denser medium compared to a vacuum. Despite this, Newton was able to explain reflection and refraction.

Huygens’ Wave Theory

Until Christopher Huygens proposed his wave theory of light in the early 18th century, no one had dared to challenge Newton’s corpuscular theory. According to Huygens’ theory, light consists of waves that travel through a very dilute and highly elastic material medium present everywhere in space, known as ether.

The density of the medium would be very low, and the modulus of elasticity would be very high, resulting in a very high speed of light.

Huygens’s wave theory successfully explained phenomena such as reflection, refraction, interference, and diffraction of light; however, it failed to explain:

1. Huygens assumed that light waves are mechanical disturbances which are longitudinal in nature, leading to polarization.

2. Black Body Radiation

3. Photoelectric Effect

4. Compton Effect

5. If hypothetical medium ether had not been discovered, we would not have known that light can propagate in a vacuum.

Huygens’ Principle: An Overview

Maxwell’s Electromagnetic Theory

According to Maxwell, light is not a mechanical wave. It is an electromagnetic wave which is transverse in nature and has a finite speed given by Maxwell’s equations.

(\begin{array}{l}C=\frac{3\times {{10}^{8}}{}^{m}}{\sqrt{{{\mu }_{0}}{{\varepsilon }_{0}}}}\end{array})

μ_o = 4π x 10^-7

εₒ = 8.854 x 10⁻¹²

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Wavefront and Wave Normal

What is Wavefront?

Wavefront is a cloud-based monitoring and analytics platform that provides real-time visibility into the performance of cloud and on-premises applications. It helps organizations to quickly identify and fix application performance issues, and improve customer experience.

A wavefront is defined as the locus of all points of the medium which vibrate in the same phase. There are three types of wavefronts, depending on the shape of the source of light.

Spherical Wave Front

When light is emerging from a point source, the wavefronts are spherical in shape.

In spherical wavefronts,

The amplitude of light waves, (A \propto \frac{1}{r}).

And, the intensity of light waves, $I \propto \frac{1}{r^2}$

Cylindrical Wave Front

When the source of light is linear, the wavefronts take on a cylindrical shape. All points are equidistant from the source.

The amplitude of light waves, (A \propto \frac{1}{\sqrt{r}})

Intensity of light waves (I \propto \frac{1}{r})

Plane Wave Front

When the light is coming from a very far-off source, the wavefronts are planar. For a plane wavefront, Amplitude remains constant therefore Intensity also remains constant.

Important JEE Main Questions on Optics

![Optics - Important JEE Main Questions]()

Top 10 Most Important and Expected Questions on Wave Optics for JEE

What is Wave Normal?

Wave Normal is a web-based platform that provides an easy-to-use, interactive tool for creating, editing, and sharing audio recordings. It is designed to be used by both professionals and amateurs alike.

A wave normal is a perpendicular drawn to the surface of a wavefront at any point, in the direction of propagation of light. This is the same as a ray of light, which is the direction in which light travels.

Shape of Wavefronts

A lens can be used to alter the shape of wavefronts. The concept of wavefronts in regards to reflection and refraction is explained in detail below.

Wavefronts for Reflection

If light falls on a plane mirror:

• It will be reflected in the same direction, with the same angle of incidence and angle of reflection.

The shape of the wavefront of the reflected light, if the plane wavefronts are being reflected on a plane mirror, is again planar.

If light falls on a concave mirror:

• The light rays will be reflected inward and converge at a single point.

If light falls on a convex mirror:

• The light rays will be reflected outward and diverge away from a single point.

If a plane wavefront falls on a concave mirror, the shape of the reflected light is spherical.

If a plane wavefront falls on a convex mirror, the shape of the reflected light is spherical.

Refraction of Wavefronts

If light falls on plane surfaces:

If a plane wavefront falls on a plane surface, the refracted ray will also have a plane wavefront.

If Light Falls on Curved Surfaces:

The emergent light from a plane wavefront that falls on a converging or diverging lens will have a spherical wavefront.

Answer:

Check Your Understanding:

The direction of propagation of the wave is along the normal vector to the plane (\begin{array}{l}\overrightarrow{n}=\frac{1}{\sqrt{3}}\left( \begin{array}{c}1\-1\end{array}\right)\end{array} ).

Solution: Given, $$y=8-\sqrt{3}x,$$ which is a straight-line equation. So, the wavefront can be represented as a straight line having a slope $$\tan \theta =-\sqrt{3}.$$

As it has a negative slope, the wavefront is represented as:

/\

The wavefront makes an angle of 150° with the x-axis. Therefore, the wave will make an angle of 60° with the x-axis, as it must be perpendicular to the wavefront.

Huygens’ Principle

According to Huygen’s principle, every point on a given wavefront can be viewed as a new source of disturbance which emits its own spherical wavelets known as secondary wavelets. These secondary wavelets propagate in all directions with the same speed as the wave.

At any instant (Δt), if a surface touches the secondary wavelets tangentially in the forward direction, the position and shape of the new wavefront at that instant is known as a “secondary wavefront”.

As discussed in the introduction, Huygen’s principle of secondary wavelets could explain many optical phenomena such as reflection, refraction, interference, and diffraction. However, it could not explain why wavefronts of secondary wavelets are formed in the forward direction, rather than the backward direction.

Interference of Light

The effect of two superimposed light waves causing a non-uniform energy distribution in the medium is called interference.

Coherent vs. Incoherent Sources

Coherent Sources: Two sources that emit a monochromatic light continuously with a constant phase difference between them are referred to as coherent sources.

Corrected Statement: The sources which do not emit light with a consistent phase difference are referred to as incoherent sources.

Video Lessons

Young’s Double Slit Experiment

![Young’s Double Slit Experiment]()

Superposition of Waves

![Superposition of Waves]()

Power Transmitted by a Wave

![Power Transmitted by a Wave]()

Ray Optics: Reflection from a Plane Mirror - Quick Overview

##Frequently Asked Questions on Wave Optics

What is the meaning of Diffraction in Wave Optics?

Diffraction is a phenomenon in which a wave passes through a slit or obstacles and bends around the end of the obstacle or through an aperture. This results in the wave entering the geometrical shadow of the obstacle.

What is the difference between constructive and destructive interference?

Constructive interference: If two waves approach in such a way that their crests line up together, the resultant wave will have a higher amplitude.

Destructive interference: When a crest of one wave meets the trough of another wave, it is known as destructive interference. The resulting wave will have a low amplitude.

Wave optics is a branch of physics that deals with the behavior and properties of light and other electromagnetic waves.

In Wave Optics or Physical Optics, a branch of Optics, phenomena such as Polarization, Diffraction, Interference, etc. are studied where Ray Approximation of Geometric Optics is not applicable.