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PHY 1109 – Lecture 1 Notes

Topic: Introduction of Physical Optics, Nature of Light, Theories of Light, Huygens’ Principle and Construction

1. Physical Optics

Definition: Branch of optics that studies the wave properties of light such as interference, diffraction, and polarization.
Difference from Geometrical Optics:
- Geometrical optics → ray model, explains reflection, refraction, image formation.
- Physical optics → wave model, explains phenomena where ray theory fails.
Importance: Essential for understanding modern optical instruments, lasers, fiber optics, and communication systems.

2. Nature of Light

Light has been studied through three major theoretical models:

(a) Corpuscular Theory (Newton)

Light consists of tiny, massless, perfectly elastic particles emitted from luminous bodies.
Explains: rectilinear propagation, reflection, refraction.
Fails to explain: interference, diffraction, partial reflection and refraction at the same surface, polarization.

(b) Wave Theory (Huygens, Fresnel)

Light is a wave propagating through a hypothetical medium (luminiferous ether).
Explains: interference, diffraction, polarization.
Fails to explain: photoelectric effect, blackbody radiation.

(c) Quantum Theory of Light (Planck, Einstein, Modern View)

Light consists of discrete packets of energy called photons, with energy (E = h \nu).
Explains: photoelectric effect, Compton scattering, blackbody radiation.
Supports wave-particle duality:
- Wave nature → interference, diffraction.
- Particle nature → emission and absorption in quanta.

📌 Modern physics accepts dual nature of light → both wave and particle characteristics coexist.

3. Huygens’ Principle

Formulated by Christiaan Huygens (1678) to explain propagation of light waves.
Statement: Each point on a given wavefront acts as a source of secondary spherical wavelets. After a certain time, the new wavefront is the tangent surface to these secondary wavelets.

(a) Key Concepts

Wavefront: Surface joining all points vibrating in the same phase.
- Types:
  - Plane wavefront (from distant source).
  - Spherical wavefront (from point source).
Secondary Wavelets: Small spherical waves emitted from every point on a wavefront.
Envelope: The common tangent to all wavelets gives the new position of the wavefront.

Maxwell electromagnetic wave equation:

… .

Michaelson Morley experiment:

Etger doesn’t exist

Additional:

(b) Laws Derived from Huygens’ Principle

Law of Reflection:
- Angle of incidence = angle of reflection.
- Derivation: Construct secondary wavelets on reflecting surface, show path difference symmetry.
Law of Refraction (Snell’s Law):
- $(n_{1} sin i = n_{2} sin r)$ .
- Derivation: Construct secondary wavelets at interface between two media, compare velocities.
Rectilinear Propagation of Light:
- In homogeneous medium, wavefronts remain plane or spherical, explaining straight-line propagation.

Additional:

4. Construction of New Wavefront (Huygens’ Construction)

Step 1: Start from an initial wavefront AB.
Step 2: Consider points A, B, … on AB as sources of secondary wavelets.
Step 3: After time (t), radius of each wavelet = (vt) where (v) = velocity of light in medium.
Step 4: Draw circles (2D) or spheres (3D) with radius (vt).
Step 5: The common tangent to all wavelets gives the new wavefront CD.

Applicable to:

Plane wavefront propagation.
Spherical wavefront propagation.
Reflection and refraction at boundaries.

5. Significance

First clear wave-based explanation of light propagation.
Foundation of interference and diffraction theory.
Still used in modern physics as a qualitative tool for understanding wave behavior.

Key Takeaways

Light requires both wave and particle theories for a complete description.
Huygens’ Principle → every point on a wavefront is a source of secondary waves.
Using this principle, reflection and refraction laws can be derived.
This lecture builds the foundation for later study of interference, diffraction, and polarization.

PHY 1109 – Lecture 1 Glossary

Physical Optics

Physical Optics: Branch of optics that studies phenomena where the wave nature of light is essential, e.g., interference, diffraction, polarization.
Geometrical Optics: Optics treating light as rays; explains reflection, refraction, image formation but not interference or diffraction.

Nature of Light

Corpuscular Theory: Light is made of tiny particles (corpuscles) emitted by luminous bodies.
Wave Theory: Light is a wave propagating through a medium (ether).
Quantum Theory: Light consists of photons (energy quanta), exhibiting both particle and wave properties.
Photon: A discrete particle of light carrying energy (E = h\nu).
Wave-Particle Duality: Concept that light exhibits both wave-like and particle-like behaviors.

Wave Concepts

Wavefront: A surface joining points of a wave vibrating in the same phase.
Plane Wavefront: Flat wavefront, typical for waves from a distant source.
Spherical Wavefront: Curved wavefront, radiating from a point source.
Secondary Wavelets: Small spherical waves emitted from points on a wavefront (Huygens’ principle).
Envelope: The tangent surface to all secondary wavelets, forming the new wavefront.

Propagation Laws

Law of Reflection: Angle of incidence equals angle of reflection.
Angle of Incidence (i): Angle between incident ray and normal to the surface.
Angle of Reflection (r): Angle between reflected ray and normal.
Law of Refraction (Snell’s Law): ( n_1 \sin i = n_2 \sin r ); light bends when entering a medium with different refractive index.
Refractive Index (n): Ratio of light speed in vacuum to speed in a medium: ( n = c/v ).
Rectilinear Propagation: Light travels in straight lines in a homogeneous medium.

Huygens’ Principle / Construction

Huygens’ Principle: Every point on a wavefront acts as a source of secondary wavelets; the new wavefront is the tangent to these wavelets.
Wavelet Radius (vt): Distance a secondary wavelet travels in time (t), where (v) is wave velocity in the medium.
Construction of Wavefront: Method of drawing secondary wavelets and tangent to determine new position of the wavefront.

Minor Terms / Supporting Concepts

Luminiferous Ether: Hypothetical medium once believed necessary for wave propagation.
Phase: Position of a point in its oscillation cycle at a given time.
Propagation: Movement of a wave through space or medium.
Medium: Material (solid, liquid, gas, or vacuum) through which light or waves travel.
Tangential Surface: Surface that touches all secondary wavelets at a single point without cutting through them.

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1109 – Lecture 1 Notes