2 Properties of Light

Light is modeled as both an electromagnetic wave and a particle. As a wave, light has electric and magnetic fields that oscillate perpendicular to its direction of travel. The oscillation has an immutable frequency, ν₀ (s^–1), but its speed, c, and wavelength, λ (m), change depending on the medium through which the wave travels (Eqn. 2.1). The speed of light in a vacuum is c₀ (= 2.998 × 10⁸ m/s) and n is the refractive index of the medium. Although it might be best to characterize light by its frequency, it is much more common to discuss light in terms of wavelength.

(Eqn. 2.1)        [latex]c = c_{0}/n = λv_{0}[/latex]

A particle of light is a photon and carries energy, E (Eqn. 2.2), that is proportional to its wave-like property of frequency (or inversely proportional to wavelength), where h (= 6.63 × 10^–34 J s) is Planck’s constant. The amplitude of a light wave is a measure of the number of photons, but not the energy of those photons.

(Eqn. 2.2)        [latex]E = hv_{0} = h(c_{0}/λ)[/latex]

Light and other electromagnetic radiation are often categorized according to photon energy, measured on a wavelength scale: ultraviolet (UV; 100–400 nm), visible (400–700 nm), near-infrared (NIR; 700 nm–3 µm), mid-infrared (3–20 µm), and more. To some extent, these categories correspond to the way in which the light interacts with atoms and molecules.

Light-Matter Interactions

Light interacts with matter in several ways, some of which are best described with the wave model and some of which are best described with the particle model. Conceptually, most light-matter interactions relate to the electric field of photons interacting with the electric fields of molecules and atoms. Several interactions of light with matter and with itself are described below.

Absorption: Atoms and molecules may absorb photons, converting the energy of these photons into other forms of energy (e.g. potential energy, heat). The absorption of selected wavelengths of light is one the main mechanisms by which materials exhibit visible colour (often appearing the colour complementary to the one that is most strongly absorbed).

Scattering: Particles may interact with photons and redirect them. If redirection occurs without a change in photon energy it is called elastic scattering. The details of the scattering depend, in part, on the size of the particle. To a first approximation, Rayleigh scattering occurs with particles smaller than the wavelength of light (e.g. atoms, molecules) and Mie scattering mechanisms occur with particles equal or larger than the wavelength of light.

Reflection: When a beam (or ray) of light encounters a boundary between two different media (e.g. air-glass interface), some fraction of light reflects off this boundary at an angle equal to the angle of incidence. Reflection can be very efficient (e.g. a mirror) or minimal (e.g. transparent glass).

Refraction: When a beam (or ray) of light encounters a boundary between two different media (e.g. an air-glass interface), some fraction of light passes through the boundary at an angle different than the angle of incidence. (Snell’s Law is the relationship between the angle of incidence and the angle of refraction.) Refraction is a consequence of light changing speeds in different media. The refractive index of a medium, n, is a wavelength-dependent measure of how much light slows down in a medium relative to vacuum. Values of n are always ≥ 1.

Diffraction: When a wave of light encounters an obstacle or aperture similar in size to its wavelength, it spreads out radially as if it were a new point source of light waves. This behaviour has several important consequences for interference between light waves.

Interference: When two light waves overlap with one another in space, their oscillations superimpose and produce a new net oscillation. For the interference to be constructive (i.e. waves augment one another) the oscillations must be in phase with one another (i.e. the crests and troughs of the oscillations overlap in both time and space). Destructive interference or a beat pattern will occur otherwise.

Connections

The above behaviours of light have important roles in spectroscopic methods and instruments, which use light as the stimulus and/or measured response for the analyte(s).

• The absorption of light by molecules (Ch. 6) is useful for measuring analyte concentrations (Ch. 7) and reporting on molecular structure (Ch. 12)
• This chapter introduced elastic scattering. Inelastic scattering (Ch. 14) is a means of obtaining chemical information
• Diffraction and interference are the working principles of the most common types of monochromators and filters for wavelength selection (Ch. 4)
• Interference between light waves is the basis of the Michelson interferometer for infrared spectroscopy (Ch. 13)
• Lenses and mirrors use refraction and reflection (respectively) to collect, focus, collimate, or otherwise direct light within an instrument (Ch. 7, Ch. 9, Ch. 11, Ch. 13, Ch. 15)

Methods of analysis that use light as the stimulus and response are typically non-destructive and non-invasive, and the instruments can sometimes be made with smaller size and lower cost than other methods. With this versatility, light-based methods of analysis are quite popular.

Post-Reading Questions

1. A red laser has a wavelength of 638 nm and a green laser has a wavelength of 532 nm. Do the photons in the green laser beam have more or less energy than the photons in the red laser beam?
2. BK7 is a common type of glass for manufacturing lenses and has a refractive index of n ≈ 1.5 for visible light. Air has a refractive index of n ≤ 1.0003 for visible wavelengths. Is the wavelength of a red laser beam within a BK7 glass lens longer or shorter than when the laser beam travels through air?
3. The leaves of many plants and trees appear green in sunlight. Does this observation imply that leaves absorb green light most strongly?
4. An instrument technician wants to bend a laser beam 90° from its original straight-line trajectory. At what angle should a mirror be placed?
5. What phenomenon do optical lenses use to focus light?
6. Some spectrophotometer designs feature slits with widths on the order of millimeters. Do you anticipate seeing a diffraction pattern when visible light (ca. 400–700 nm wavelength) passes through these slits?

Topic Learning Objectives

The chapter is a primer for the following learning objectives, which will be covered in lecture and/or with additional assigned reading:

• Match the qualitative behaviours of light with quantitative descriptions (e.g. equations) for the same behaviour.
• Be prepared to classify light-matter interactions as best corresponding to wave-like behaviour or particle-like behaviour.
• Identify when the wave nature of light and when the quantum nature of light is leveraged for the operation of photonics technologies.
• Be prepared to identify select behaviours of light in simple diagrams of instruments.
• Match the energies associated with regions of the electromagnetic spectrum with processes associated with molecular, atomic, and sub-atomic structure.
• Convert (via calculation) between the energies, wavelengths, and frequencies of photons.