Basic Optics

Abstract

1.1 Introduction This chapter on optics provides the reader with the basic understanding of light rays and light waves, image formation and aberrations, interference and diffraction effects, and resolution limits that one encounters because of diffraction. Laser sources are one of the primary sources used in various applications such as interferometry, thermography, photoelasticity, and so on, and Section 1.10 provides the basics of lasers with their special characteristics. Also included is a short section on optical fibers since optical fibers are used in various applications such as holography, and so on. The treatment given here is condensed and short; more detailed analyses of optical phenomena can be found in many detailed texts on optics [1–6]. 1.2 Light as an Electromagnetic Wave Light is a transverse electromagnetic wave and is characterized by electric and magnetic fields which satisfy Maxwell's equations [1, 2]. Using these equations in free space, Maxwell showed that each of the Cartesian components of the electric and magnetic field satisfies the following equation: ∇ 2 = ε 0 μ 0 ∂ 2 ∂t 2 (1.1) where ε 0 and μ 0 represent the dielectric permittivity and magnetic permeability of free space. After deriving the wave equation, Maxwell could predict the existence of electromagnetic waves whose velocity (in free space) is given by c = 1 √ ε 0 μ 0 (1.2) Since ε 0 = 8.854 × 10 −12 C 2 N −1 m −2 and μ 0 = 4π × 10 −7 Ns 2 C −2 (1.3) we obtain the velocity of light waves in free space c = 1 √ ε 0 μ 0 = 2.99794 × 10 8 ms −1 (1.4) In a linear, homogeneous and isotropic medium, the velocity of light is given by v = 1 √ εμ (1.5) where ε and μ represent the dielectric permittivity and magnetic permeability of the medium. The refractive index n of the medium is given by the ratio of the velocity of light in free space to that in the medium n = εμ ε 0 μ 0 (1.6) In most optical media, the magnetic permeability is very close to μ 0 and hence we can write Eq. (1.6) as n ≈ ε ε 0 = √ K (1.7) where K represents the relative permittivity of the medium, also referred to as the dielectric constant. The most basic light wave is a plane wave described by the following electric and magnetic field variations: