Wave Optics

10.1 INTRODUCTION

The chapter on Wave Optics begins with a historical overview of the models of light. In 1637, Descartes proposed the corpuscular model of light, which explained reflection and refraction by treating light as particles. According to this model, if a light ray bends towards the normal upon refraction, the speed of light in the second medium would be greater. Isaac Newton further developed this corpuscular theory in his book "Opticks," which popularized the particle nature of light for a long time. In 1678, Christiaan Huygens proposed the wave theory of light, which provided a different explanation. The wave model predicted that if the refracted ray bends towards the normal, the speed of light in the second medium is less, contrary to the corpuscular model. This was experimentally confirmed by Foucault in 1850, who showed that light travels slower in water than in air, supporting the wave theory. Despite its explanatory power, the wave theory was not immediately accepted because of Newton's authority and the belief that waves require a medium for propagation, while light travels through vacuum. The wave nature of light was firmly established by Thomas Young's interference experiment in 1801, which measured the wavelength of visible light to be extremely small (for example, yellow light has a wavelength of about 0.6 micrometers). Because the wavelength of visible light is very small compared to the size of typical optical components, light can be approximated as traveling in straight lines, which is the basis of geometrical optics. Geometrical optics neglects the wave nature by assuming the wavelength tends to zero, and defines rays as paths of energy propagation. Later, Maxwell's electromagnetic theory of light unified electricity, magnetism, and optics by predicting electromagnetic waves that propagate in vacuum at the speed of light. Maxwell showed that light waves are electromagnetic waves consisting of oscillating electric and magnetic fields that sustain each other, allowing propagation through vacuum. This chapter focuses on the wave theory of light, starting with Huygens' principle to derive laws of reflection and refraction, then discussing interference based on superposition, diffraction based on Huygens-Fresnel principle, and finally polarization, which arises from the transverse nature of light waves.

• Descartes' corpuscular model explained reflection and refraction treating light as particles.
• Huygens' wave theory predicted speed of light decreases in denser media, confirmed experimentally.
• Young's interference experiment established the wave nature of light and measured wavelength.
• Geometrical optics approximates light as rays ignoring wavelength effects.
• Maxwell's electromagnetic theory unified light as electromagnetic waves propagating in vacuum.
• Wave optics explains phenomena like interference, diffraction, and polarization.
• 📌 Corpuscular model: Light as particles explaining reflection and refraction.
• 📌 Wave theory: Light as waves explaining interference and diffraction.
• 📌 Geometrical optics: Approximation treating light as rays ignoring wavelength.

10.2 Huygens PRINCIPLE

Huygens' principle is a fundamental concept in wave optics that helps determine the position and shape of wavefronts at any time. A wavefront is defined as a surface of constant phase where all points oscillate in phase. For example, when a stone is dropped in water, circular wavefronts spread out from the point of impact, with all points on a circle oscillating in phase. For a point source emitting waves uniformly in all directions, the wavefronts are spherical surfaces centered on the source, called spherical waves. At large distances, a small portion of a spherical wavefront can be approximated as a plane wave. Huygens' principle states that every point on a wavefront acts as a source of secondary wavelets that spread out in all directions with the speed of the wave. The new wavefront at a later time is the envelope (common tangent) of all these secondary wavelets. For example, consider a spherical wavefront at time t=0. Drawing spheres of radius vτ (v is wave speed, τ is time interval) from each point on the wavefront, the common tangent to these spheres gives the new wavefront at time t=τ. This construction can be used for spherical and plane waves. One subtlety is the absence of a backward wave (backwave) in the wavefront propagation. Huygens assumed the amplitude of secondary wavelets is maximum in the forward direction and zero backward, an ad hoc assumption later justified by rigorous wave theory. The rays of light are defined as lines normal to the wavefronts, indicating the direction of energy propagation. Huygens' principle provides a geometric method to understand wave propagation and forms the basis for deriving laws of reflection and refraction.

• Wavefront: surface of constant phase where all points oscillate in phase.
• Spherical wavefronts originate from point sources; plane waves approximate spherical waves far away.
• Huygens' principle: every point on a wavefront acts as a source of secondary wavelets.
• New wavefront is the envelope (common tangent) of secondary wavelets after time τ.
• Rays are normals to wavefronts, indicating direction of energy propagation.
• Backwave absence explained by amplitude being zero in backward direction (Huygens' assumption).
• 📌 Wavefront: Surface of constant phase in a wave.
• 📌 Secondary wavelets: Small spherical waves emitted from points on a wavefront.
• 📌 Envelope: Common tangent surface to secondary wavelets forming new wavefront.