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Physics · Class 12 Science

Ch 10Wave Optics — Class 12 Physics, concept-first.

The study of wave optics begins with a fundamental question: What is light? The corpuscular model was first put forward in 1637 by René Descartes, who used it to derive Snell's law of refraction.

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Key concepts

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Frequency Invariance

When a light wave crosses from one medium into another — on reflection or on refraction — one property never changes: its frequency.

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Chapter contents

The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.

10.1

Introduction

The study of wave optics begins with a fundamental question: What is light? The corpuscular model was first put forward in 1637 by René Descartes, who used it to derive Snell's law of refraction.

10.2

Huygens Principle

A wavefront is a surface of constant phase. All points on a wavefront oscillate in phase. For a point source emitting waves uniformly in all directions, the wavefronts are spheres (spherical wave).

10.3

Refraction and Reflection of Plane Waves using Huygens Principle

Huygens Principle explains how a wavefront propagates. Every point on a wavefront acts as a source of secondary spherical wavelets.

10.3.1

Refraction of a Plane Wave

Huygens principle states that every point on a wavefront acts as a source of secondary spherical wavelets. The new wavefront is the envelope of these wavelets.

10.3.2

Refraction at a Rarer Medium

When a plane wave travels from a denser medium into a rarer medium, the wave speed increases (). This change in speed causes the wavefront to bend away from the normal.

10.3.3

Reflection of a Plane Wave by a Plane Surface

When a plane wavefront strikes a flat reflecting surface, the reflected wavefront can be constructed using Huygens' principle.

+Worked Examplesi1 question
  1. Example 10.1(a) When monochromatic light is incident on a surface separating two media, the reflected and refracted light both have the same frequency a…Preview
10.4

Coherent and Incoherent Addition of Waves

When two or more waves overlap in space, the principle of superposition applies: the resultant displacement at any point is the vector sum of the displacements due to each individual wave.

10.5

Interference of Light Waves and Young's Experiment

Light from an ordinary source (like a sodium lamp) undergoes abrupt, random phase changes every seconds.

10.6

Diffraction

Diffraction is the bending of waves around the edges of an obstacle or aperture. It is a universal property of all waves — sound, water, light, and matter waves.

10.6.1

The Single Slit

When a narrow slit is illuminated by a monochromatic (single-wavelength) light source, the light does not travel in a perfectly straight line.

10.6.2

Seeing the Single Slit Diffraction Pattern

The single‑slit diffraction pattern is not just a textbook idea — you can observe it at home with simple items. The key is that the slit width must be comparable to the wavelength of light (about m).

10.7

Polarisation

Polarisation is a property unique to transverse waves — waves where the oscillation is perpendicular to the direction of propagation.

+Worked Examplesi1 question
  1. Example 10.2Discuss the intensity of transmitted light when a polaroid sheet is rotated between two crossed polaroids?Preview

Summary

- Huygens' Principle: Every point on a wavefront acts as a source of secondary spherical wavelets; the new wavefront is the envelope of these wavelets.

Points to Ponder

1. Wavefronts vs. Rays: A point source emits waves that spread spherically in all directions, yet we often observe light traveling in straight, narrow rays.

Exercises

+Show 10 questions10 questions
  1. 10.1Monochromatic light of wavelength $589\ \text{nm}$ is incident from air on a water surface. What are the wavelength, frequency and speed of…Free
  2. 10.2What is the shape of the wavefront in each of the following cases: (a) Light diverging from a point source. (b) Light emerging out of a conv…Free
  3. 10.3(a) The refractive index of glass is $1.5$. What is the speed of light in glass? (Speed of light in vacuum is $3.0 \times 10^{8}\ \text{m s}…Free
  4. 10.4In a Young's double-slit experiment, the slits are separated by $0.28\ \text{mm}$ and the screen is placed $1.4\ \text{m}$ away. The distanc…Preview
  5. 10.5In Young's double-slit experiment using monochromatic light of wavelength $\lambda$, the intensity of light at a point on the screen where p…Preview
  6. 10.6A beam of light consisting of two wavelengths, $650\ \text{nm}$ and $520\ \text{nm}$, is used to obtain interference fringes in a Young's do…Preview
  7. 10.7In a double-slit experiment the angular width of a fringe is found to be $0.2^\circ$ on a screen placed $1\ \text{m}$ away. The wavelength o…Preview
  8. 10.8What is the Brewster angle for air to glass transition? (Refractive index of glass = $1.5$.)Preview
  9. 10.9Light of wavelength $5000\ \text{Å}$ falls on a plane reflecting surface. What are the wavelength and frequency of the reflected light? For…Preview
  10. 10.10Estimate the distance for which ray optics is good approximation for an aperture of $4\ \text{mm}$ and wavelength $400\ \text{nm}$.Preview

Additional Exercises

+Show 11 questions11 questions
  1. 10.11The $6563\ \text{Å}$ H$_\alpha$ line emitted by hydrogen in a star is found to be red-shifted by $15\ \text{Å}$. Estimate the speed with whi…Free
  2. 10.12Explain how Corpuscular theory predicts the speed of light in a medium, say, water, to be greater than the speed of light in vacuum. Is the…Free
  3. 10.13You have learnt in the text how Huygens' principle leads to the laws of reflection and refraction. Use the same principle to deduce directly…Free
  4. 10.14Let us list some of the factors, which could possibly influence the speed of wave propagation: (i) nature of the source. (ii) direction of p…Preview
  5. 10.15For sound waves, the Doppler formula for frequency shift differs slightly between the two situations: (i) source at rest; observer moving, a…Preview
  6. 10.16In double-slit experiment using light of wavelength $600\ \text{nm}$, the angular width of a fringe formed on a distant screen is $0.1^\circ…Preview
  7. 10.17Answer the following questions: (a) In a single slit diffraction experiment, the width of the slit is made double the original width. How do…Preview
  8. 10.18Two towers on top of two hills are $40\ \text{km}$ apart. The line joining them passes $50\ \text{m}$ above a hill halfway between the tower…Preview
  9. 10.19A parallel beam of light of wavelength $500\ \text{nm}$ falls on a narrow slit and the resulting diffraction pattern is observed on a screen…Preview
  10. 10.20Answer the following questions: (a) When a low flying aircraft passes overhead, we sometimes notice a slight shaking of the picture on our T…Preview
  11. 10.21In deriving the single slit diffraction pattern, it was stated that the intensity is zero at angles of $n\lambda/a$. Justify this by suitabl…Preview

Exemplar Problems

Higher-order thinking / exemplar-style practice problems.

+Show 20 questions20 questions
  1. Q1Consider sunlight incident on a slit of width $10^4\ \text{\AA}$. The image seen through the slit shall (a) be a fine sharp slit white in co…Free
  2. Q2Consider a ray of light incident from air onto a slab of glass (refractive index $n$) of width $d$, at an angle $\theta$. The phase differen…Free
  3. Q3In a Young's double slit experiment, the source is white light. One of the holes is covered by a red filter and another by a blue filter. In…Free
  4. Q4A standard Young's two-slit arrangement has slits $S_1$ and $S_2$ illuminated by a monochromatic source $S$. On the screen, $P$ is the centr…Preview
  5. Q5Two sources $S_1$ and $S_2$ of intensities $I_1$ and $I_2$ are placed in front of a screen. The intensity distribution observed across the c…Preview
  6. Q6Consider sunlight incident on a pinhole of width $10^3\ \text{\AA}$. The image of the pinhole seen on a screen shall be (a) a sharp white ri…Preview
  7. Q7Consider the diffraction patern for a small pinhole. As the size of the hole is increased (a) the size decreases. (b) the intensity increase…Preview
  8. Q8For light diverging from a point source (a) the wavefront is spherical. (b) the intensity decreases in proportion to the distance squared. (…Preview
  9. Q9Is Huygen's principle valid for longitudunal sound waves?Preview
  10. Q10Consider a point at the focal point of a convergent lens. Another convergent lens of short focal length is placed on the other side. What is…Preview
  11. Q11What is the shape of the wavefront on earth for sunlight?Preview
  12. Q12Why is the diffraction of sound waves more evident in daily experience than that of light wave?Preview
  13. Q13The human eye has an approximate angular resolution of $\phi = 5.8 \times 10^{-4}\ \text{rad}$ and a typical photoprinter prints a minimum o…Preview
  14. Q14A polariod (I) is placed in front of a monochromatic source. Another polatiod (II) is placed in front of this polaroid (I) and rotated till…Preview
  15. Q15In a two-slit interference arrangement the slits $S_1$ and $S_2$ are separated by a distance $2D$; their midpoint is $C$ so that $S_1C = CS_…Preview
  16. Q16A monochromatic source $S$ emitting unpolarised light illuminates a two-slit arrangement with slits $S_1$ and $S_2$. A polariser $P$, whose…Preview
  17. Q17In a two-slit interference set-up a source $A$ sends light to two slits $S_1$ and $S_2$ whose midpoint is $C$, with $S_1C = S_2C = d$ (slit…Preview
  18. Q18Four identical, mutually coherent monochromatic point sources $A$, $B$, $C$, $D$ emit waves of the same wavelength $\lambda$, all in phase.…Preview
  19. Q19The optical properties of a medium are governed by the relative permitivity ($\varepsilon_r$) and relative permeability ($\mu_r$). The refra…Preview
  20. Q20To ensure almost 100 per cent transmittivity, photographic lenses are often coated with a thin layer of dielectric material. The refractive…Preview

Sample & Board Papers

Sample papers and previous-year board questions for this subject.

+Show 3 questions3 questions
  1. Q1Draw a graph showing the intensity distribution of fringes due to diffraction at single slit.Preview
  2. Q2(a) When an unpolarized light of intensity $I_o$ is passed through a polaroid, what is the intensity of the linearly polarized light? Does i…Preview
  3. Q3(i) Write two points to distinguish between interference and diffraction fringes. (ii) In a Young's double slit experiment, fringes are obta…Preview