### Category: Optics

Interference of Light Waves

## Introduction to Interference of Light

When two light waves of same frequency or wavelength having the same phase or constant phase difference travelling simultaneously through a medium get superimposed, then the available energy is redistributed producing bright and dark patch on the screen. This phenomena is known as interference of light.

This phenomena of interference of light waves was discovered by English Scientist Thomas Young in 1801. Interference of light waves supports the wave theory of light. Interference of light waves supports the wave nature of light.

## Principle of superposition of light wave

When two or more light waves are travelling simultaneously through a medium or space, the resultant displacement at point and at a given time due to all the waves is given by the vector sum of the individual displacements produced by each wave separately at the same time. This is known as principle of superposition of light wave.

If y1, y2, y3, …. , yn are the displacement made by ‘n’ number of waves separately at a given point in same time then according to superposition of light wave, the resultant displacement at that point at same time is given by, y = y1 + y2 + y3 + …. + yn

## Types of interference of light wave

1. ### Constructive interference

The condition of interference when the crest of two waves overlaps each other and trough of two waves overlap each other is Constructive Interference. In the constructive interference of light waves, the amplitude becomes maximum and hence the light is intensified.

Constructive interference occurs when the path difference of two waves is equal to integral multiple of wavelength.
i.e. x = nλwhere n = 0, 1, 2, ….

2. ### Destructive interference

The condition of interference when the crest of one wave overlaps with the trough of another wave is Destructive Interference. In destructive interference of light wave, the amplitude becomes minimum and hence the intensity of light becomes zero.

Destructive interference occurs when the path difference of two waves is equal to integral multiple of half of wavelength.
i.e. x = (2n-1)λ/2, where n = 1, 2, 3, ….

## Conditions for Sustained Interference of Light Waves

• Two light sources must be coherent.
• Waves should have certain path difference.
• Two light waves must have same frequency and amplitude.
• Two coherent sources of light must lie very close to each other.
• Light sources must be coherent.
• Both light waves must be in the same state of polarization.
• Sources of light must be monochromatic i.e. both source of light must emit light of same wavelength.

## Explanation for Interference of Light Waves

When light waves of same frequency and amplitude from two sources gets superimposed, the distribution of energy in a certain plain becomes uneven. This is due to different interference (constructive and destructive) at different points. This can be shown by a simple experiment which was originally given by Thomas Young in 1802.

Originally, a monochromatic source of light is passed through a small slit ‘S’. So, this slit acts as incoherent source. Then the light waves propagate ahead and strike other two slits ‘S1‘ and ‘S2‘ act as a coherent source of light since light waves crossing these slits have same frequency and amplitude.

Then two slits S1 and S2 diffract light waves. Diffracted light waves get superimposed and condition of interference is obtained. In the above figure, dotted lines act as the crests of light waves and solid lines act as the trough of light waves. After superimposing of two waves, alternate bright and dark fringes are obtained.

Constructive interference occurs at the points where crest-crest and trough-trough of two waves meet. Amplitude of light wave becomes maximum at such points and a bright fringe is obtained. It is shown in the figure by denoting with the word ‘Max’. Similarly, destructive interference occurs at the points where crest-trough of two waves meet. Amplitude of light wave becomes zero at such points and a dark fringe is obtained. It is shown in the figure by denoting with the word ‘Min’.

Hence, alternate pattern of bright and dark fringe is obtained due to interference of light waves. This supports the Huygen’s wave theory of light.

## Application of Interference of Light Waves

• It is used to determine the refractive index or thickness of transparent thin sheets.
• It is used to determine the wavelength of light precisely.
• It is used in holography to produce three dimensional images.
• It was initially used to disprove the existence of ‘ether’.
Parabolic mirror

## Introduction

A mirror which has reflecting surface in the shape of parabola is called parabolic mirror. As the mirror can converge accurately a wide parallel beam of light at the focus,parabolic mirrors are used to increase the intensity of reflected beam. Such beams reflected by parabolic mirrors remains undiminished to a long distance. Parabolic mirrors are free from spherical aberration and hence don’t form caustic curve.

## Need for parabolic mirror

If a fine beam of light is incident on a spherical mirror of small aperture, the rays of light meet at a single point after reflection to form the image of a point object. However, if the mirror is large and the beam of light is wide, the light rays do not focus at a single point.  They cross each other in the different points in the principal axis. The rays near the axis are called parallax rays and are focused near the pole. The rays towards the margin are called marginal rays and are focused farther from the focus. Hence these rays intersect each other at various points which lie in a curve called caustic curve as shown in figure. The caustic curve has a cusp at the focus of the mirror.

Conversely, if a point source of light is placed at the focus of spherical mirror, all the rays reflected by the mirror wouldn’t be parallel to each other and the intensity of the light decreases.

This kind of defect in spherical mirror is spherical aberration. To make our ‘devices’ free from such defect parabolic mirrors are designed.

## Working of parabolic mirror

Parabolic mirrors are so constructed that each and every beam coming from infinity falling in mirror are brought to be focused in the principal focus of the mirror. In this way, parabolic mirrors remove spherical aberration in spherical mirrors.

Similarly, if a point source of light is placed in the focus of the parabolic mirror, the reflected rays are parallel to principal axis. So they can travel a long distance along the principal axis.