# Wave Optics

## What is Wave Optics?

Wave optics stands as a witness for a famous standoff between two great scientific communities who dedicated their lives to understand the nature of light. One supports the particle nature of light; the other supports the wave nature. Sir Isaac Newton stands as a prominent figure that supported the voice of particle nature of light, who proposed corpuscular theory which states that, “light consists of extremely light and tiny particles known as corpuscles which travel with very high speeds from the source of light to create sensation of vision by reflecting on the retina of the eye”. Using this theory Newton was able to explain reflection and refraction but failed to explain the cause of interference, diffraction and polarization. The major failure of Newton’s corpuscular theory is it could not explain why velocity of light is lesser in denser medium compared to vacuum.

### Huygens Wave Theory

No one dared to challenge Newton’s corpuscular theory until Christopher Huygens proposed his wave theory of light in early 18th century. According to Huygens theory, light consists of waves which travel through a very dilute and highly elastic material medium present everywhere in space”. This medium is called as ether. As the medium is supposed to be very dilute and highly elastic, its density would be very low and modulus of elasticity would be very high so that speed of the light would be very large.

Huygens wave theory could able to explain the phenomena like reflection, refraction, interference and diffraction of light. But failed to explain:

1. Polarization as Huygens assumed light waves to be mechanical disturbances which are longitudinal in nature.
2. Black body radiation, photo electric effect and Compton Effect.
3. Hypothetical medium ether which was never discovered and now we know light can propagate in vacuum.

### Maxwell Electromagnetic Theory

According to Maxwell, light is not a mechanical wave. It is an electromagnetic wave which is transverse in nature which travels with a finite speed given by

$C=\frac{1}{\sqrt{{{\mu }_{0}}{{\varepsilon }_{0}}}}=3\times {{10}^{8}}{}^{m}/{}_{s}$

## Wavefront and Wave Normal

### What is Wavefront?

A wavefront is defined as the laws of all points of the medium which vibrate in the same phase. Depending on the shape of the source of light, wavefronts can be of three types.

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

In spherical wavefront,

Amplitude of light waves, $A\propto \frac{1}{r}$

and, Intensity of light waves, $I\propto \frac{1}{{{r}^{2}}}$

#### Cylindrical Wave Front

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

In this case, 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 remains constant.

### What is Wave Normal?

A perpendicular drawn to the surface of a wavefront at any point, in the direction of propagation of light, is called as “wave normal”. The direction in which light travels is called as a ‘ray’ of light. Thus, a wave normal is same as a ray of light.

### Shape of Wavefronts

A lens can be used to change the shape of wavefronts. The concept of wavefronts for reflection and refraction is explained below.

#### Wavefronts For Reflection

• If light falls on a plane mirror:

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

• If light falls on a concave mirror; convex mirror:

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.

#### Wavefronts For Refraction

• If light falls on plane surfaces:

If a plane wave front falls on a plane surface the refracted ray will also have a plane wave front.

• If light falls on curved surfaces:

If a plane wavefront falls on a converging (or) diverging lens, the emergent light will have a spherical wavefront.

A wavefront is represented by the plane $y=8-\sqrt{3}x$. Find the direction of propagation of the wave.

Solution: Given, $y=8-\sqrt{3}x,$ which is 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 like

∴ wavefront makes an angle of $150{}^\circ$ with x-axis. As wave must be perpendicular to wavefront, it will make an angle of $60{}^\circ$ with the x-axis.

### Huygen’s Principle

According to Huygen’s principle, Every point on a given wavefront can be regarded as a fresh source of new disturbance and sends out its own spherical wavelets called secondary wavelets. These secondary wavelets spread out in all directions with the velocity of the wave. A surface touching these secondary wavelets tangentially in the forward direction at any instant $\left( \Delta t \right)$ gives the position and shape of the new wavefront at the instant. This is called “secondary wavefront”.

As discussed in the introduction Huygen’s principle of secondary wavelet’s could able to explain many optical phenomena like reflection, refraction, interference, and diffraction, but could not explain why wavefronts of secondary wavelets are formed in forward direction not in backward direction.

### Coherent and Incoherent Sources

Two sources which emit a monochromatic light continuously with a zero (or) constant phase difference between them are called coherent sources. The sources which do not emit light with constant phase difference are called as Incoherent sources.

$S=\frac{D}{d}\left( \mu -1 \right)t$