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Wave optics is the branch of optics that studies interference, diffraction, polarization, and other phenomena for which the geometric optics ray approximation is inapplicable.
- It is also known as Physical optics.
- It covers all aspects of wave characteristics of light and its behavior.
- Ray approximation of geometric optics is impossible without considering wave optics.
- According to the Wave Theory of Light, light is a form of a transverse wave whose nature of propagation depends upon the medium through which it travels.
- In wave optics, the approximation is accomplished by using ray optics to estimate the field on a surface.
- It also involves combining the ray-estimated field over a mirror, lens, or aperture to calculate the scattered or transmitted field.
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Key Terms: Newton’s Corpuscular Theory, Wavefront, Maxwell’s electromagnetic wave theory, Interference, Superposition of waves, Wavelets, Light, Ray optics, Speed of light
Wave Optics Theory
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Wave optic theories have been proposed by many eminent scientists to prove that light is a form of a wave as opposed to those theories which state light has a particle nature.
- It was Einstein’s Light Quantum Theory which proved that light has both particle and wave nature.
- Sir Issac Newton was one of the first scientists ever who proposed the Corpuscular theory to state that light has a wave nature.
- Important wave optics theories are given below.
Newton’s Corpuscular Theory
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Light consists of a very small invisible elastic particle that travels in a vacuum and the speed of vacuum is 3 x 108 m/s.
- The concept could explain refraction and reflection.
- The size of the corpuscular of other colors of light is another.
- It could not clarify interference, polarisation, diffraction, photoelectric effect, and Compton Effect.
- The concept failed as it could not clarify why light travels quicker in a rarer medium than in a denser medium.
Newton’s Corpuscular Theory
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Wavefront
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A wavefront is clarified as the continuous locus of all the particles of a medium, which are vibrating in the same area.
The shape of the wavefront depends upon the shape of the source of distribution.
Types of Wavefront
These are three categories of wavefront
- Spherical wavefront: If the source of disturbance is a point source then the wavefront is spherical.
- Cylindrical wavefront: If the source of disturbance is a line source, then the wavefront is cylindrical.
- Plane wavefront: At a very large distance from the point source, a small part of the spherical wavefront appears plane and this part of the spherical wavefront is called a plane wavefront.
Types of Wavefront
Huygens Wave Theory
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In 1678, Dutch physicist Christian Huygens put forth a wave theory of light.
- According to this theory, light is a periodic disturbance transmitted through a medium in the form of waves.
- He assumed that the medium through which light travels is Lumiferous ether.
- According to him, medium ether is pervadic space including vacuum and it has very high elasticity.
Huygens' wave theory describes light phenomena such as reflection, refraction, interference, and diffraction. However, he failed to explain the following:
- Huygens thought that light waves, which are longitudinal in nature, are mechanical disturbances, which lead to polarization.
- Black body radiation, the photoelectric effect, and the Compton effect are all examples of electromagnetic radiation.
- The hypothetical medium ether was never discovered, and we now know that light can travel in a vacuum.
Huygens Principle
Huygens's principle gives geometrical details of the traveling of a wave. According to Huygens’s principle
- Each source of light is a center of disturbance from which waves spread in all directions.
- All particles equidistant from the source and vibrating in the same phase lie on a surface known as a wavefront.
- Evergy point in a wavefront is a source of new disturbance which produces secondary wavelets.
- These wavelets are spherical and travel with the speed of light in all directions in that medium.
- Only forward envelopes enclosing the tangents at the secondary wavelets at any instant give the new position of the wavefront.
Huygen’s Wave Theory
Maxwell’s Electromagnetic Wave Theory
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According to Maxwell’s electromagnetic wave theory
- Light is a type of electromagnetic wave that does not require a material medium for its circulation.
- Light waves feel polarisation because of their transverse nature.
- An electromagnetic wave in a vacuum has a velocity that is c = 1 / √μo εo
- The velocity of electromagnetic waves in a medium is less than that of light, v < c v = 1 / √μo εo εr μr = c / √μo εr
- On average, the velocity of electromagnetic waves depends upon the magnetic and electric properties of the medium.
Maxwell’s Electromagnetic Wave Theory
Max Planck’s Quantum Theory
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According to Max Planck’s quantum theory
- Light emits from a source in the form of packets of energy called photons or quanta.
- The power of a photon is E = hv, where h is Planck’s continuous and v is the frequency of light.
- Quantum concepts could clarify the photoelectric effect, Raman Effect, and Compton Effect.
- Quantum concept failed to clarify interference, polarisation, and diffraction of light.
Superposition of Waves
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When two equal waves propagate in a medium concurrently, then at any point the resultant displacement is similar to the vector sum and displacement shaped by individual waves.
According to the superposition of waves
y = y1 + y2
Interference of Light
Something that happens at every place and at every moment, Interference is a very natural phenomenon.
- Yet interference patterns are not visible everywhere.
- Interference is a phenomenon where two waves superpose to form the resultant wave of the lower, higher, or same amplitude.
- Optical interference or light interference is the most commonly seen interference.
- That’s because light waves are randomly generated every which way by most sources.
- This means that there is no constant amplitude, frequency, or phase of the light waves coming out of a source.
- To give an easy example of interference of light, it would be the soap bubble which reflects wide colors when illuminated by a light source.
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Things to Remember
- Light consists of a very small invisible elastic particle that travels in a vacuum and the speed of the vacuum is 3 x 108 m/s.
- A wavefront is clarified as the continuous locus of all the particles of a medium, which are vibrating in the same area.
- Wavefront can be categorized into Cylindrical wavefront, Spherical wavefront, and Plane wavefront.
- Light travels in a medium in the method of the wavefront.
- A wavefront is the locus of all the bits vibrating in the equal phase.
- A kind of electromagnetic wave, Light waves do not demand a material medium for their circulation.
- Light waves feel polarisation because of their transverse nature.
- Light emits from a source in the form of packets of energy called photons or quanta.
- Interference is a phenomenon where two waves superpose to form the resultant wave of the lower, higher, or same amplitude.
- Optical interference or light interference is the most commonly seen interference.
Previous Year Questions
- When hydrogen atom is in its first excited level, its radius, is….
- When an electron does transition from n=4 to n=2 , then emitted line spectrum will be…...
- α -particle consists of….
- An electron of a stationary hydrogen atom passes from the fifth energy level….
- Complete the equation for the following fission process…. [NEET 1998]
- using non-relativistic approach, the speed of electron in this orbit will be…. [NEET 2015]
- When the glancing angle of incidence of light on a material is...[COMEDK UGET 2004]
- Two waves having intensity ratio 25 : 4 produce interference. The ratio of maximum to minima intensity is...[COMEDK UGET 2004]
- In Young's double slit experiment,1st dark fringe occurs directly...[COMEDK UGET 2009]
- In the diffraction pattern due to a single slit linear width of the central max...[COMEDK UGET 2007]
- In Newton ring experiment, monochromatic light is replaced by white light...[COMEDK UGET 2008]
- In diffraction through a single slit experiment, slit width is halved...[COMEDK UGET 2004]
- Which of the following is false for interference of light?...[JKCET 2012]
- Which of the following is true for the minimum angular separation of two stars...[JKCET 2012]
- Values for Brewster's angle can be...[JKCET 2015]
- Unpolarized light falls on two polarizing sheets placed one on top of other….[JKCET 2013]
- In Young's double slit experiment using monochromatic light of wavelength \(\lambda\) ….[AMUEEE 2018]
- In a single-slit diffraction experiment, the width of the slit is reduced by...[JKCET 2012]
- the wavelength of light illuminating the slits is….[JKCET 2013]
- Colours in thin films are due to….[JKCET 2008]
Sample Questions
Ques. The position among the pass axis of the polarizer and the clarify is 45°, write the ratio of the intensities of essential light and the transmitted light after passing through the analyzer. (2 marks)
Ans. I = \(\frac{I_0}{2} cos^2 \theta\)
…...where [I0 is the originial intensity and θ is the angle between the axis of the polariser and the analyser]
∴ \(\frac{I}{I_0} = \frac{cos^2\theta}{2} = \frac{1}{4}\) [ (\(\because\)θ = 45o, cos2 45o = 1/2)]
Ques. What category of wavefront will appear from a
(i) point source, and
(ii) distant light source?(2 marks)
Ans. (i) Point source – Spherical wavefront
(ii) Distant light source – Plane wavefront.
Ques. The Unpolarised light is an event on a flat surface of a glass of refractive index µ at an angle i. Uncertainty the reproduced light gets completely polarized, write the relation between the angle i and refractive index µ.(1 mark)
Ans. µ = tan ip.
Ques. Make a diagram to show the refraction of a flat wavefront event in a convex lens and hence draw the refracted wavefront.(2 marks)
Ans. 
Wave Theory
Ques. Definition of the term wavefront?(1 mark)
Ans. The locus of all such bits of the medium which are vibrating in an equal direction is called a wavefront.
Ques. Give the relation between path other and wavelength for constructive interference between two waves.(1 mark)
Ans. For constructive interference, the path other between two waves should be an integral many of λλ i.e., p=nλ,n=0,1,2,3,......
Ques. State two settings to obtain continued interference of light.(2 marks)
Ans. The two settings to obtain continued interference of light are as follows-
(a) the nature of the two light sources should be coherent
(b) the two light sources should be placed close to each other and should be narrow.
Ques. Why are coherent bases important to present a sustained interference pattern?(1 mark)
Ans. Coherent sources have a continuous phase others. This confirms that the location of minima and Maxima do not change with time i.e., a continued interference pattern is obtained.
Ques. Is there any difference between the colors developing from a prism and the colors of a soap film seen in sunlight?(1 mark)
Ans. Of course. In the prism, colors are present due to the dispersion of light.
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