Physics STD12

Wave Optics

October 5, 2023
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Class 12 Physics

Terms and Definitions

Terms and Definitions in Wave Optics

  1. Wavefront: A wavefront is an imaginary surface that connects all the points of a wave that are in the same phase (i.e., have the same oscillation or vibration at a given instant). It is often represented as a line or surface.
  2. Huygens’ Principle: Huygens’ principle states that every point on a wavefront can be considered as a source of secondary spherical waves, and the envelope of these secondary waves represents the new wavefront at a later time.
  3. Diffraction: Diffraction is the bending of waves as they encounter an obstacle or aperture. It results in the spreading of waves around corners and the formation of interference patterns.
  4. Interference: Interference occurs when two or more waves superpose (combine) to form a resultant wave. It can be constructive (waves reinforce each other) or destructive (waves cancel each other out).
  5. Coherence: Coherence refers to the property of light waves having a constant phase relationship. It is essential for producing stable interference patterns.
  6. Polarization: Polarization refers to the orientation of the oscillations of light waves in a particular direction. Unpolarized light contains waves vibrating in all directions, while polarized light consists of waves vibrating in a single plane.
  7. Young’s Double-Slit Experiment: Young’s experiment is a classic experiment that demonstrates the interference of light waves. It involves shining light through two closely spaced slits, which produces an interference pattern on a screen.
  8. Single-Slit Diffraction: Single-slit diffraction occurs when light passes through a narrow slit, and it leads to the spreading of light waves, resulting in a diffraction pattern on a screen.
  9. Fresnel Diffraction: Fresnel diffraction is a more general case of diffraction that accounts for both near-field and far-field effects when light waves encounter obstacles or apertures.
  10. Fraunhofer Diffraction: Fraunhofer diffraction refers to the diffraction pattern produced when light waves pass through a single narrow slit and are observed at a distance far from the slit. It results in a simple diffraction pattern.
  11. Diffraction Grating: A diffraction grating is a device consisting of closely spaced parallel slits or rulings that produce a series of bright and dark lines (spectral lines) when light is diffracted through it. It is used for spectral analysis.
  12. Dispersion: Dispersion is the separation of light into its component colors (spectrum) due to the different wavelengths of light bending by different amounts when passing through a medium, such as a prism.
  13. Newton’s Rings: Newton’s rings are a series of concentric colored rings formed when light is reflected between a plano-convex lens and a flat glass plate. They are used to determine the thickness of a thin film.
  14. Optical Path Difference (OPD): The optical path difference is the difference in the distances that two rays of light travel when they pass through different parts of an optical system. It is crucial in interference and diffraction phenomena.

Introduction

ATOQ (ANY TIME ONLINE QUIZ) – SET-1

Certainly! Here are 20 multiple-choice questions (MCQs) related to terms and definitions in wave optics. I’ll provide the questions, and you can try to answer them. The answers are not provided here, so you can test your knowledge or use them for self-assessment.

  1. What is the term for an imaginary surface connecting points of a wave in the same phase?
    A) Wavelength
    B) Wavefront
    C) Amplitude
    D) Frequency
  2. Which principle states that every point on a wavefront can be considered as a source of secondary spherical waves?
    A) Fermat’s Principle
    B) Huygens’ Principle
    C) Snell’s Law
    D) Newton’s Law of Motion
  3. What phenomenon causes the bending of waves as they encounter an obstacle or aperture?
    A) Reflection
    B) Refraction
    C) Diffraction
    D) Dispersion
  4. When two waves superpose to form a resultant wave, it is called:
    A) Diffraction
    B) Polarization
    C) Interference
    D) Dispersion
  5. Coherence refers to the property of light waves having a constant:
    A) Amplitude
    B) Phase relationship
    C) Frequency
    D) Wavelength
  6. Which classic experiment demonstrates the interference of light waves by passing light through two closely spaced slits?
    A) Newton’s Rings
    B) Single-Slit Diffraction
    C) Young’s Double-Slit Experiment
    D) Fraunhofer Diffraction
  7. What is the term for the orientation of the oscillations of light waves in a particular direction?
    A) Diffraction
    B) Dispersion
    C) Polarization
    D) Interference
  8. Fraunhofer diffraction occurs when:
    A) Light passes through a single narrow slit.
    B) Light passes through a double-slit.
    C) Light reflects off a mirror.
    D) Light encounters a prism.
  9. What optical device consists of closely spaced parallel slits or rulings that produce spectral lines when light is diffracted through it?
    A) Prism
    B) Diffraction Grating
    C) Lens
    D) Mirror
  10. Which term refers to the separation of light into its component colors due to different wavelengths of light bending by different amounts in a medium?
    A) Polarization
    B) Dispersion
    C) Diffraction
    D) Interference
  11. What phenomenon produces a series of concentric colored rings when light is reflected between a lens and a flat glass plate?
    A) Polarization
    B) Dispersion
    C) Newton’s Rings
    D) Interference
  12. The difference in the distances traveled by two rays of light is called:
    A) Wavelength
    B) Frequency
    C) Amplitude
    D) Optical Path Difference (OPD)
  13. Which principle states that light follows the path that takes the least time to travel between two points?
    A) Huygens’ Principle
    B) Fermat’s Principle
    C) Snell’s Law
    D) Ohm’s Law
  14. A diffraction grating produces a pattern of bright and dark lines known as:
    A) Newton’s Rings
    B) Fraunhofer Diffraction
    C) Interference Fringes
    D) Spectral Lines
  15. What term describes the bending of light as it passes from one medium to another at an angle?
    A) Dispersion
    B) Diffraction
    C) Reflection
    D) Refraction
  16. In the context of wave optics, what does OPD stand for?
    A) Optical Path Difference
    B) Oscillation Phase Difference
    C) Optical Propagation Distance
    D) Observational Path Deviation
  17. What type of interference occurs when two waves combine to increase the overall amplitude of the resultant wave?
    A) Constructive Interference
    B) Destructive Interference
    C) Polarized Interference
    D) Refractive Interference
  18. When light passes through a narrow slit and results in a diffraction pattern, it is known as:
    A) Double-Slit Diffraction
    B) Huygens’ Diffraction
    C) Single-Slit Diffraction
    D) Fraunhofer Diffraction
  19. The spreading of waves around corners due to diffraction is a result of:
    A) Refraction
    B) Polarization
    C) Interference
    D) Diffraction
  20. What law governs the change in direction of light when it passes from one medium into another with a different refractive index?
    A) Newton’s Law
    B) Huygens’ Law
    C) Snell’s Law
    D) Ohm’s Law

Study Notes

HUYGEN’S PRINCIPLE

Wave front enveloping the secondary sources of light and new wave front enveloping the secondary wavelets
  • Huygen’s principle helps to locate the new position and shape of the wavefront at any instant.
A spherical wave starting from a point source
  • Focus – a fixed point or the centre of the circle
  • Locus – moving point of a circle. Locii – a plural form of locus i.e., moving points.
  • Wavefront
    • locus of points which oscillate in phase
    • a surface of constant phase
  • Spherical waves
    • waves emitted uniformly in all directions
    • the locus of points which have the same amplitude (wave height) and vibrate in same phase
    • have spherical shape
  • Plane waves
    • At a larger distance from the source, a small portion of the sphere is considered as a plane. Such waves are called plane waves.
  • The Huygen’s principle is basically a geometrical construction.
  • A1, A2, A3 represent the spherical wavefront with O as the centre at time, t = 0.
  • F1, F2, F3 represent the new spherical wavefront with A1, A2 and A3 as centre and F1, F2 and F3 are in forward positions, but D1, D2 and D3 are backwave, actually they do not exist.

REFRACTION OF A PLANE WAVE

AB = incident wavefront

CD = refracted wavefront

i = incident angle

r = refracted angle

v1 = velocity of light in medium-1 (rarer medium)

v2 = velocity of light in medium-2 (denser medium)

Refraction at a rarer medium

REFLECTION OF A PLANE WAVE BY A PLANE SURFACE

According to law of reflection angle incidence = angle of refraction.

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THE DOPPLER EFFECT

The apparent change in frequency noticed by an observer whent there is a relative motion between the observer and the moving source of light is called Doppler effect.

When there is an increase in wavelength, the Doppler effect is called red shift.

When there is a decrease in wavelength, the Doppler effect is called blue shift.

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THE COHERENT AND INCOHERENT ADDITION OF WAVES

  • Interference if one of the properties of light.
  • It is based on the superposition principle.
  • Superposition at a particular point in the medium is the resultant displacement produced by a number of waves and it is the vector sum of the displacements produced by each of the waves.
Image result for principle of superposition

When two wave trains superimpose each other they may result either constructive interference resulting bright spot or destrcutive interference resulting dark spot.

Image result for interference pattern
Source: Encyclopedia Britannica

Interference of light waves and Young’s double slit experiment

When two sodium lamps illuminate two pinholes S1 and S2, there is no intereference pattern on the screen.

Interference pattern was noticed when a single source of light is made to fall on two narrow nearby slits (double slits). These two slits are considered to be coherent sources of light and hence interference was noticed.
S1, S2 = doulbe slit acts coherent sources of light. GG’ = screen on which the interference is observed. d = the small distance between the two narrow slits (coherent sources), D = distance between the coherent sources and the screen. P = the arbitrary point where maximum intensity is observed by intereference on the screen. x = distance beteween P and the centre of the intereference pattern, O.

When x and d << D, the denominator S2P + S1P = 2D

For the constructive interference (bright fringes)

The distance between two consecutive dark fringes or bright fringes is called fringe width, w. It is a constant.

  • D and d are constants.
  • Fringe width is directly proportional to wavelength.
  • The fringe width for red light (longer wavelength) is greater than that of blue light (shorter wavelength)

The intensity distribution in Young’s double slit experiment to explain interference.

Interference – Concept Video

DIFFRACTION

  • S = Source of light
  • LN = width of single slit
  • Path difference = NP – LP
  • NP – LP = QP
  • L and N = two edges of the single slit
  • M1, M2 = two point on the slit plane separated by a distance, y
  • MC = normal to the slit plane
Image result for diffraction pattern
The double slit intefrence pattern where the envelope shows the single slit diffraction.

DIFFERENCE BETWEEN INTEFERENCE AND DIFFRACTION

INTERFERENCEDIFFRACTION
1. Superposition of a few secondary wavelets1. Superposition of large number of secondary waves.
2. Fringes are equally spaced.2. Wide near the obstacle and becomes narrow towards the shadow region.
3. Result of interaction of two different wavefronts originating from coherent sources.3. Result of interaction between different parts of the same wavefront.
4. Points of minimum intensity are perfectly dark.4. Points of minimum intensity are shaded and not perfectly dark.
5. All bright fringes or bands are of uniform intensity.6. They are not of same intensity.

NOTE:
Energy is conserved in both interference and diffraction by redistributing the light energy by producing dark and bright fringes.

Resolving power of optical instruments

  • The ability of the instrument to produce distinctly separate images of two close objects.
Image result for resolving power of telescope
  • Rayleigh – Two point objects A and B are resolved, when central maximum of diffraction patter of B lies on first secondary minimum of diffraction pattern of A.
  • Limit of resolution of an optical instrument – It is the minimum distance between two objects, which can be visible as separate identitites by the optical instruments.

Resolving power of a microscope

  • f = focal length of the lens
  • 2a = diameter of the lense (Circular aperture)
  • A parallel beam of light falls on a convex lens. Because of diffraction effects, the beam gets focused to a spot of radius as given below.

Resolving power depends on the following parameters.

Resolving power of telescope

POLARISATION

  • In ordinary light, the vibrations of electric vector take place in all possible direction in a plane perpendicular to the direction of propagation of light.
  • Polarisation – the phenomenon of restricting vibrations of light in a particular direction, perpendicular to the direction of wave propagation.
  • Nicol or tourmaline crystal acts as a polariser.

Law of Malus

When polarised light is incident on an analyser, the resultant intensity of light (I) transmitted from the analyser is directly proportional to the square of the cosine of the angle between the plane of transmission of analyser and polariser.

Polarisation of light by reflection

The angle of incidence at which the reflected light is completely plane polarised is called the polarising angle (Brewster’s angle).

Wave Characteristics of light

Huygen’s principle

ATOQ – SET-2

Concept – Hugen’s Principle and Wave Characteristics

MCQs:

  1. According to Huygens’ principle, every point on a wavefront becomes a _.
    a) Secondary source of wavelets
    b) Absorber of wave energy
    c) Transparent medium
    d) Incoherent source of light
  2. Which of the following phenomena can be explained by Huygens’ principle?
    a) Polarization of light
    b) Reflection of light
    c) Photoelectric effect
    d) Nuclear fusion
  3. Huygens’ principle is used to explain the _.
    a) Particle nature of light
    b) Interference of light
    c) Refraction of light
    d) Photoelectric effect
  4. Which property of light can be explained using Huygens’ principle?
    a) Speed of light
    b) Color of light
    c) Dispersion of light
    d) Magnetic properties of light
  5. When light waves encounter a boundary between two media at an angle, they may change direction due to _.
    a) Reflection
    b) Refraction
    c) Polarization
    d) Diffraction
  6. In Huygens’ principle, what is a wavelet?
    a) A small boat on a wave
    b) A unit of energy in a wave
    c) A small portion of a wavefront
    d) A type of interference pattern
  7. Huygens’ principle helps explain the _ of light waves.
    a) Diffraction
    b) Dispersion
    c) Photoelectric effect
    d) Doppler effect
  8. The bending of light waves as they pass from air into water is an example of _.
    a) Polarization
    b) Diffraction
    c) Refraction
    d) Reflection
  9. Which characteristic of light determines its color?
    a) Amplitude
    b) Frequency
    c) Speed
    d) Wavelength
  10. What happens to the wavelength of light when it passes from air into glass?
    a) It decreases
    b) It increases
    c) It remains the same
    d) It becomes zero
  11. The phenomenon of interference occurs when _.
    a) Two light waves have the same frequency
    b) Light reflects off a surface
    c) Light passes through a polarizer
    d) Light undergoes refraction
  12. What is the speed of light in a vacuum?
    a) 3 x 10^8 meters per second
    b) 3 x 10^6 meters per second
    c) 3 x 10^10 meters per second
    d) 3 x 10^4 meters per second
  13. The angle of incidence is equal to the angle of reflection according to _.
    a) Snell’s law
    b) Huygens’ principle
    c) Fermat’s principle
    d) Newton’s theory of light
  14. Which type of wave can propagate through a vacuum?
    a) Transverse waves
    b) Longitudinal waves
    c) Electromagnetic waves
    d) Sound waves
  15. The change in direction of light when it passes through a lens is due to _.
    a) Reflection
    b) Diffraction
    c) Dispersion
    d) Refraction
  16. Which color of light has the shortest wavelength in the visible spectrum?
    a) Red
    b) Green
    c) Blue
    d) Yellow
  17. When light waves superpose destructively, they _.
    a) Reinforce each other
    b) Produce a bright spot
    c) Cancel each other out
    d) Create interference fringes
  18. The phenomenon of diffraction is most pronounced when the size of the obstacle or slit is _.
    a) Large compared to the wavelength of light
    b) Small compared to the wavelength of light
    c) Equal to the wavelength of light
    d) Irrelevant to the wavelength of light
  19. Which of the following is a property of both particles and waves?
    a) Polarization
    b) Refraction
    c) Diffraction
    d) Electric charge
  20. In the double-slit experiment, what does the interference pattern demonstrate about the nature of light?
    a) It proves that light is composed of particles.
    b) It shows that light is a continuous wave.
    c) It suggests that light exhibits both wave and particle properties.
    d) It confirms that light travels in straight lines.

Ray Diagram

Total Internal Reflection

Interference part-1

Interference part-2

Resolving power of Telescope

Polarisation of Light

KEY-1

  1. B) Wavefront
  2. B) Huygens’ Principle
  3. C) Diffraction
  4. C) Interference
  5. B) Phase relationship
  6. C) Young’s Double-Slit Experiment
  7. C) Polarization
  8. A) Light passes through a single narrow slit.
  9. B) Diffraction Grating
  10. B) Dispersion
  11. C) Newton’s Rings
  12. D) Optical Path Difference (OPD)
  13. B) Fermat’s Principle
  14. B) Fraunhofer Diffraction
  15. D) Refraction
  16. A) Optical Path Difference
  17. A) Constructive Interference
  18. C) Single-Slit Diffraction
  19. D) Diffraction
  20. C) Snell’s Law

Key-2

Certainly! Here are the answers to the 20 multiple-choice questions (MCQs) on Huygens’ principle and the wave characteristics of light:

Key:

  1. a) Secondary source of wavelets
  2. b) Reflection of light
  3. c) Refraction of light
  4. c) Dispersion of light
  5. b) Refraction
  6. c) A small portion of a wavefront
  7. a) Diffraction
  8. c) Refraction
  9. d) Wavelength
  10. a) It decreases
  11. a) Two light waves have the same frequency
  12. a) 3 x 10^8 meters per second
  13. b) Huygens’ principle
  14. c) Electromagnetic waves
  15. d) Refraction
  16. c) Blue
  17. c) Cancel each other out
  18. b) Small compared to the wavelength of light
  19. c) Diffraction
  20. c) It suggests that light exhibits both wave and particle properties.