Introduction to Wave Optics

# Introduction to Wave Optics | Physics Class 12 - NEET PDF Download

 Table of contents Wave Optics Newton’s Corpuscular Theory Wavefront Huygen’s Wave Theory Maxwell’s Electromagnetic Wave Theory Max Planck’s Quantum Theory De – Broglie’s Dual Theory Superposition of Waves Coherent Sources of Light

## Wave Optics

Wave optics describes the connection between waves and rays of light. According to the wave theory of light, the light is a form of energy which travels through a medium in the form of transverse wave motion. The speed of light in a medium depends upon the nature of the medium.

## Newton’s Corpuscular Theory

• Light consists of very small invisible elastic particles which travel in vacuum with a speed of 3 x 108 m/s.
• The theory could explain reflection and refraction.

Newton's Corpuscular Theory

• The size of corpuscular of different colours of light are different.
• It could not explain interference, diffraction, polarization. photoelectric effect and Compton effect. The theory failed as it could not explain why light travels faster in a rarer medium than in a denser medium.

## Wavefront

A wavefront is defined as the continuous locus of all the particles of a medium, which are vibrating in the same phase.

These are three types:

• Spherical wavefront
• Cylindrical wavefront
• Plane wavefront

Wavefront

## Huygen’s Wave Theory

• Light travel in a medium in the form of wavefront.
• A wavefront is the locus of all the particles vibrating in same phase.
• All particles on a wavefront behaves as a secondary source of light, which emits secondary wavelets.

Huygen's Principle

• The envelope of secondary wavelets represents the new position of a wavefront.
• When source of light is a point source,the wavefront is spherical.
• Amplitude (A) is inversely proportional to distance (x) i.g., A ∝ 1 / x .
∴ Intensity (I) ∝ (Amplitude)2
• When Source of light is linear, the wavefront is cylindrical.
• Amplitude (A) ∝ 1 / √x
∴ Intensity ∝ (Amplitude)2 ∝ 1 / x

### Huygen’s Principle

• Every point on given wavefront (called primary wavefront) acts as a fresh source of new disturbance called secondary wavelets.
• The secondary wavelets travels in all the directions with the speed of light in the medium.
• A surface touching these secondary wavelets tangentially in the forward direction at any instant gives the new (secondary) wave front of that instant.

Question for Introduction to Wave Optics
Try yourself:
What is a wavefront?

## Maxwell’s Electromagnetic Wave Theory

• Light waves are electromagnetic waves which do not require a material medium for their propagation.
• Due to transverse nature, light wave undergo polarisation.
• The velocity of electromagnetic wave in vacuum is c = 1 / √μo εo.
• The velocity of electromagnetic waves in medium is less than that of light, v < c
v = 1 / √μo εo εr μr = c / √μo εr
• The velocity of electromagnetic waves in a medium depend upon the electric and magnetic properties of the medium.
where, μo = absolute magnetic permeability and
εo = absolute electrical permittivity of free space.

Electromagnetic Spectrum

• It failed to explain the phenomenon of photoelectric effect, Compton effect and Raman effect.

## Max Planck’s Quantum Theory

• Light emits from a source in the form of packets of energy called quanta or photon.
• The energy of a photon is E == hv, where h is Planck’s constant and v is the frequency of light.
• Quantum theory could explain photoelectric effect, Compton effect and Raman effect.
• Quantum theory failed to explain interference, diffraction and polarization of light.

## De – Broglie’s Dual Theory

• Light waves have dual nature, wave nature according to Maxwell’s electromagnetic wave theory and particle nature according to Max-Planck’s quantum theory.
• Two natures of light are like the two faces of a coin. In anyone phenomena only its one nature appears.
• Energy of photon = hv = hc / λ
where, h = Planck’s constant 6.6 * 10<sup-34 J / s
de-Broglie wave equation is λ = h / p = h / mv
where h denotes Planck’s constant.

## Superposition of Waves

When two similar waves propagate in a medium simultaneously, then at any point the resultant displacement is equal to the vector sum of displacement produced by individual waves.

y = y1 + y2

### Interference of Light

• When two light waves of similar frequency having a zero or constant phase difference propagate in a medium simultaneously in the same direction, then due to their superposition maximum intensity is obtained at few points and minimum intensity at other few points.
• This phenomena of redistribution of energy due to superposition of waves is called interference of light waves.
• The interference taking place at points of maximum intensity is called constructive interference.
• The interference taking place at points of minimum intensity is destructive interference.

### Fringe Width

• The distance between the centers of two consecutive bright or dark fringes is called the fringe width.
• The angular fringe width is given by θ = λ / d.
where λ is the wavelength of light d is the distance between two coherent sources.

Question for Introduction to Wave Optics
Try yourself:
Which theory explains the phenomenon of interference of light?

### Conditions for Constructive and Destructive Interference

➢ For Constructive Interference

• Phase difference, φ = 2nπ
• Path difference, Δx = nλ
where, n = 0, 1, 2, 3,…

➢ For Destructive Interference

• Phase difference, φ = (2n – 1)π
• Path difference, Δx = (2n – 1)π / 2
where, n = 1, 2, 3, …

If two waves of exactly same frequency and of amplitude a and b interfere, then amplitude of resultant wave is given by

R = √a2 + b2 + 2ab cos φ

where φ is the phase difference between two waves.

Rmax = (a + b)

Rmin = (a – b)

Intensity of wave

∴ I = a2 + b2 + 2ab cos φ

= I1 + I2 + 2 √I1 I2 cos φ

where I1 and I2 are intensities of two waves.

∴ I1 / I2 = a2 / b2 = ω1 / ω2

Where ω1 and ω2 are width of slits.

Energy remains conserved during interference.

Interference fringe width

β = Dλ / d

where, D = distance of screen from slits, λ = wavelength of light and d = distance between two slits.

Distance of nth bright fringe from central fringe xn = nDλ / d

Distance of nth dark fringe from central fringe x’n = (2n – 1) Dλ / 2d

## Coherent Sources of Light

The sources of light emitting light of the same wavelength, the same frequency having a zero or constant phase difference are called coherent sources of light.

Coherent sources of Light

When a transparent sheet of refractive index μ and of thickness t is introduced in one of the path of interfering waves, then fringe pattern shifts in that direction by a distance Y

Y = D / d (μ – 1) t = β / λ (μ – 1) t

where, β = fringe width.

➢ Fresnel’s Biprism

• It is a combination of two prisms of very small refracting angles placed base to base. It is used to obtain two coherent sources from a single light source.

➢ Llyod’s Mirror

• The shape of interference fringes are usually hyperbolic.
• When screen is held at 900 to the line joining focii of the hyperbola, the fringes are circular.

Llyod's Mirror

• When distance of screen (D) is very large compare to the distance between the slits (d), the Cringes are straight.
The document Introduction to Wave Optics | Physics Class 12 - NEET is a part of the NEET Course Physics Class 12.
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## Physics Class 12

105 videos|425 docs|114 tests

## FAQs on Introduction to Wave Optics - Physics Class 12 - NEET

 1. What is the difference between Newton’s Corpuscular Theory and Huygen’s Wave Theory in wave optics?
Ans. Newton's Corpuscular Theory states that light is made up of particles, while Huygen's Wave Theory proposes that light behaves as a wave. This difference in the fundamental nature of light led to the wave-particle duality concept in modern physics.
 2. How does Maxwell’s Electromagnetic Wave Theory contribute to our understanding of wave optics?
Ans. Maxwell's Electromagnetic Wave Theory describes light as electromagnetic waves, providing a comprehensive explanation for various optical phenomena such as reflection, refraction, and interference. This theory forms the basis of modern wave optics.
 3. What is the significance of Max Planck’s Quantum Theory in the context of wave optics?
Ans. Max Planck's Quantum Theory introduced the concept of quantized energy levels, which was later extended to explain the behavior of light as both waves and particles. This theory laid the foundation for the development of quantum mechanics and its application in wave optics.
 4. How does De-Broglie’s Dual Theory reconcile the conflicting theories of wave and particle nature of light in wave optics?
Ans. De-Broglie's Dual Theory suggests that all particles, including light particles, exhibit both wave and particle-like behavior. This concept helps to explain the wave-particle duality of light and provides a unified framework for understanding its behavior in wave optics.
 5. What is the significance of coherent sources of light in wave optics and how do they affect interference patterns?
Ans. Coherent sources of light emit waves that have a constant phase relationship, leading to the formation of interference patterns. These sources are crucial in studying interference and diffraction phenomena in wave optics, as they produce clear and well-defined interference fringes.

## Physics Class 12

105 videos|425 docs|114 tests

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