# Refraction of light

Authors: Anika Husen
English version by Sandra Leithäuser
back to Polarized light microscopy

## Introduction

When a ray of light passes from one material (or media) into another, refraction occurs because light travels at different speeds in different materials.

The process involves a change in wavelength because the speed of the light will change (given the energy level of the incident light). Different wavelengths will have different refraction angles and this will also change the direction of the light. This is best exemplified by the case of a prism where white light will be spread out into the spectral colors as it passes consecutively through the two interfaces, air-glass and glass-air, that are at an angle.

Refraction of light is used in polarized light microscopy. Knowing the refractive index of one of the materials or phases, it is possible to estimate the refractive index of a second one in contact with it, a useful information for its eventual identification.

## Light, waves and particles

Light is an electromagnetic radiation that behaves as a wave. Its propagation speed is c, the wave length l and the frequency f. Nevertheless, light also behaves as a particle, especially at interfaces where light is reflected (at least partially) like a ball that is thrown against a wall. These discrete energy particles are called photons and their energy is constant for a given wave frequency.

$\displaystyle E=h*f$

h is Planck´s constant with the value

$\displaystyle h = 6,626*10^{ -34}\ [Js] = 4,136*10^{ -15}\ [eVs]$

## Velocity or speed of light

The speed of light varies depending on the media it traverses. Light travels fastest in vacuum (c=1) and differs little from its speed in air, therefore these values are often equated.

$\displaystyle C_{air} = 299792458\ [m/s]$

The denser a medium, the slower an electromagnetic wave will propagate in it. The optical density (absorption) is described by the refractive index value. The refractive index (n) is the ratio between the speed of light in a vacuum and the material in consideration. Therefore, all media have a value n>1.

$\displaystyle n_x = {c_{Light} \over c_x}$

The propagation direction of light after refraction is dependent on the refractive index, n, and the angle of incidence as described by Snell´s law. The angle of incidence is the angle to the normal, i.e., the line perpendicular to the surface at the incidence point. If a ray passes from a medium with lower optical density to one of higher optical density, the angle of incidence becomes smaller, the ray is refracted and vice versa. Therefore, the ratio between the sines of the incident and refraction angles are equivalent to the ratio of the refractive indices or phase velocities.

$\displaystyle {\sin \alpha \over \sin \beta} = {v_1 \over v_2} = {n_1 \over n_2}$

## Light refraction

Light refraction occurs due to the variation of light speed within different media (as described above). When imagining a wave that moves forward within a body, lines of the same amplitude, parallel to the wavefront can be expected, if the viewing direction is perpendicular to the propagation direction.

When these parallel lines strike a boundary surface at an angle, every point of incidence produces a new vibration that will propagates in the second material and, because the light speed will be different in this material, the wavelength and the distance between the parallels of the same amplitude will also change thus changing the propagation direction.

To simplify, only parallel lines of the same amplitude are considered. If a vibration is triggered in the new material, it spreads spherically from each point. The spheres are superimposed at the tangent that intersects all surfaces of the individual waves and a new wavefront develops. Since the points, where the wave starts have intervals that depend on the wavelength and the angle of incidence, and because there is a specific time delay between the excitation of each individual point as a function of the speed within the first propagation medium, the wavefront in the second medium is orientated differently.