## Optical properties of matter

Electromagnetic waves with wavelengths λ in the range of ~400 nm to ~750 nm are called visible light.
Maxwell's equations require that the speed v of any electromagnetic wave is c = (1/(μ0ε0)½ = 3*108 m/s in free space.
Electromagnetic waves can travel through transparent media, such as water and glass.  In a medium, they interact with the atoms or molecules, and due to this interaction have an apparent speed different from c.  When electromagnetic waves travel through a transparent medium, the speed of the waves in the medium is v = c/n, where n is the index of refraction of the medium.  The index of refraction n is a property of the material.  For visible light in transparent materials n is, in general, greater than 1, so that v is less than c in the material.  In most transparent materials the index of refraction depends slightly on the wavelength of the light, and in some materials it depends on the polarization.

For light with frequency f traveling in a transparent medium we have v = λnf.
λn = λfree/n is wavelength of the light in the medium, while λfree is its wavelength in free space.

When the index of refraction changes, the wavelength of the light changes, while the frequency f stays the same.

The index of refraction n for light in air is nearly equal to 1.  For transparent materials the index of refraction listed in tables is either an average index, or it is the index for one particular wavelength.  In general, the index of refraction n varies inversely with wavelength.  It is greater for shorter wavelengths.  The table below gives the index of refraction for various wavelengths of light in glass.

Color Wavelength Index of Refraction
blue 434 nm 1.528
yellow 550 nm 1.517
red 700 nm 1.510

Most materials are not transparent to visible light, but absorb or scatter light.  Even in transparent materials a small, (or not so small, depending on the purity of the material,) fraction of the light is absorbed or scattered.

We see light because it stimulates the cells in our eyes.  Because our eyes are able to distinguish between different wavelength of light we perceive color.  If the light reaching our eyes contains a broad mixture of wavelength, we interpret it as white light.
Because light is an EM wave, it exhibits several behaviors characteristic of waves such as reflection, refraction and diffraction.

A wave front is an imaginary surface representing corresponding points of a wave that vibrate in unison.
The wave fronts of light emitted by a point source are concentric spheres, centered on the source and expanding away from the source at the speed of light.

A light ray is an imaginary directed line perpendicular to the wave front.  At a large distance from the source the curvature of the wave front can be neglected and the wave front appears flat.  The wave is then approximated by a plane wave and the light rays are parallel.

A beam of light has a non-zero width.  We usually represent it by a few rays.

In a homogeneous, isotropic medium light travels in a straight line.  When we visually perceive the world around us, we implicitly assume that light follows a straight-line path.  But when light encounters a boundary between two media with different indices of refraction, or when it travels through a non-homogeneous or non-isotropic medium, its path may not be a straight line.  If we can neglect diffraction, because all obstacles in the path of the light wave have dimensions much larger than the wavelength of the light, then we can analyze the propagation of light through different media by analyzing the path of a light ray.  This is called the ray approximation of geometrical optics.