Physics Ch15 Waves Notes Class 11

Wave Optics is a crucial chapter of Class 12 Physics that explains the wave nature of light. Unlike ray optics, which treats light as straight rays, wave optics helps us understand phenomena like interference, diffraction and polarization. 

These concepts are frequently asked in board exams, both in theory and numericals, making this chapter highly scoring if prepared properly.

According to cbse syllabus class 11 physics these notes, you’ll find clear explanations, important formulas, NCERT-based concepts, applications, common mistakes and exam-oriented questions for quick and effective revision.

Wave Optics Summarised

Earlier in Ray Optics, light was treated as rays to explain reflection and refraction. However, certain phenomena like interference and diffraction cannot be explained using ray theory. This led to the development of the wave theory of light.

Two Important Theories of Light

Following are the two important theories of light:

• Particle Theory of Light

According to this theory, light consists of tiny packets of energy called photons. It successfully explains the photoelectric effect and Compton scattering.

• Wave Theory of Light

This theory treats light as a wave phenomenon. It explains interference, diffraction, polarization and wavefront propagation.

Wave optics mainly studies light as an electromagnetic wave, where electric and magnetic fields oscillate perpendicular to each other and to the direction of propagation.

Nature of Light as an Electromagnetic Wave

Light is a transverse electromagnetic wave that travels through vacuum at a speed of c = 3 × 10⁸ m/s

Important Wave Parameters

• Wavelength (λ): Distance between two successive crests or troughs
• Frequency (f): Number of oscillations per second
• Amplitude (A): Maximum displacement of the wave
• Velocity (v): Speed of propagation of the wave

The basic wave relation is: v = fλ

Huygens’ Principle 

Huygens’ Principle is a key concept that explains wave propagation.

Statement of Huygens’ Principle

• Every point on a wavefront acts as a source of secondary wavelets
• The new wavefront is the envelope of these secondary wavelets

This principle helps explain:

• Rectilinear propagation of light
• Reflection of light
  
• Refraction of light

Interference of Light 

Interference occurs when two coherent light waves superpose, producing a pattern of bright and dark fringes.

Types of Interference

These are two types of interferences:

• Constructive Interference

Occurs when waves are in phase, resulting in maximum intensity.

Condition: Δϕ = 2nπ

• Destructive Interference

Occurs when waves are out of phase, resulting in minimum intensity.

Condition: Δϕ = (2n + 1)π

Intensity in Interference

The resultant intensity when two light waves interfere is: I = I₁ + I₂ + 2√(I₁I₂) cos ϕ, where ϕ is the phase difference between the waves. For equal intensities (I₁ = I₂ = I); Maximum intensity: I_max = 4I; and Minimum intensity: I_min = 0

Coherent Sources 

Two sources are said to be coherent if they emit waves of the same frequency and maintain a constant phase difference. For example, in Young’s Double Slit Experiment, the two slits act as coherent sources because they originate from the same source.

Young’s Double Slit Experiment

This experiment provides strong evidence for the wave nature of light.

Results of YDSE

• Alternate bright and dark fringes are formed on the screen
• Fringe width depends on wavelength, slit separation and screen distance

Important Formulas

Fringe width (β): β = λD/d; where λ = wavelength of light; D = distance of screen from slits; and d = separation between slits

Angular Fringe Width (θ): θ = λ/d

Diffraction of Light

Diffraction is the bending of light around obstacles or through narrow apertures whose size is comparable to the wavelength of light.

Types of Diffraction

• Fraunhofer Diffraction: Occurs when the source and screen are effectively at infinity (parallel rays).
• Fresnel Diffraction: Occurs when source and screen are at finite distances.

Single Slit Diffraction

The diffraction pattern consists of a central bright maximum with decreasing intensity side fringes.

Condition for Minima

a sin θ  = nλ ; where a = slit width, θ = angle of diffraction, and n = order of minima

Width of Central Maximum

The width of the central maximum in single slit diffraction is: 2λD/a; where λ = wavelength, D = distance of screen, and a = slit width

Diffraction Grating

A diffraction grating consists of a large number of equally spaced slits. Condition for Principal Maxima: d sin θ = nλ; where d = grating element (distance between adjacent slits), θ = diffraction angle, and n = order of spectrum

Gratings produce sharper and more intense maxima and are widely used in spectrometers.

Polarization of Light

Polarization restricts light vibrations to a single plane.

Important Points

• Natural light is unpolarized
• Polarized light vibrates in only one plane
• Polarization proves that light is a transverse wave

Applications of Polarization

• Polarized sunglasses
• 3D movie glasses
• Photography and glare reduction

Malus Law

When polarized light passes through an analyzer, the intensity of transmitted light is given by I = I₀ cos²θ; where I₀ = initial intensity, and θ = angle between transmission axis and polarization direction

Brewster’s Law

When light is incident at a special angle called the Brewster angle (iₚ), the reflected light becomes completely polarized. The relation is: tan iₚ = μ where μ = refractive index of the medium. At Brewster angle, the reflected and refracted rays are perpendicular to each other.

Conclusion

That’s a wrap on Wave Optics. If you clearly understand interference, diffraction and polarization, this chapter becomes one of the easiest scoring chapters in Class 12 Physics.

Revise formulas regularly, practice numericals, and don’t confuse interference with diffraction. Once your concepts are clear, boards will feel much easier. Hope this helped you revise better. Share it with a friend who’s stressed about Physics. 

FAQs

Q1. Why is light treated as a wave in Wave Optics?

Ans. Light is treated as a wave because some phenomena like interference, diffraction and polarization cannot be explained using the particle model. 

Q2. What is the main difference between interference and diffraction?

Ans. Interference occurs due to the superposition of light waves coming from two coherent sources, while diffraction occurs due to the bending of light around an obstacle or through a narrow slit.

Q3. Why do we get bright and dark fringes in Young’s double slit experiment?

Ans. Bright and dark fringes are formed due to constructive and destructive interference of light waves coming from the two slits. 

Q4. How does Huygens’ principle explain wave propagation?

Ans. According to Huygens’ principle, every point on a wavefront acts as a source of secondary wavelets. 

Q5. Why is polarization possible only for transverse waves?

Ans. Polarization restricts vibrations of light to a single plane. This is possible only if the waves vibrate perpendicular to the direction of propagation.