Refraction of light

Authors: Anika Husen
back to Polarized light microscopy

Introduction

Refraction of light occurs when a ray of light passes through the interface of two different materials at different speeds.

In doing so, the wave length and the propagation direction of the wave changes. Due to the change in speed at constant energy levels, a new wave length evolves. Because the angle of the change in direction depends on the wavelength, the light is separated into its spectral colors. On prisms the spectral colors fan out on both surfaces consecutively, because the surfaces are at an angle.

Refraction is used in polarized light microscopy. In the process, the refractive index of a phase is estimated, which is useful for identifying it.

Light, waves and particles

Light is an electromagnetic wave, and in this wave energy propels itself. It has the propagation speed c, the wave length l and the frequency f. Nevertheless, the wave behaves like a particle, especially at interfaces. Like a ball, that is thrown against a wall, the light wave is reflected (at least partially) from the surface. Also, defined energy packets appear, moving with the wave. These are described as energy quanta and have a constant energy, that depends on the frequency of the wave.

$E=h*f$

h is Planck´s constant with the value

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

Velocity or speed of light

The speed of light also varies within different media. Light travels fastest in a vacuum and its speed differs little from the speed of light in air, therefore both speeds are often equated.

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

The slower an electromagnetic wave propagates within a medium, the more optically dense is the medium. The optical density (absorption) is described with the value of the refractive index. The refractive index is the ratio between the speed of light inside a vacuum and the material to be considered. The speed of light in the vacuum has the value 1, all other media have the value n>1.

$n_{x}={c_{Light} \over c_{x}}$

According to snells law, the angle of the new propagation direction (after refraction), is dependent on n and the ray´s angle of incidence. The angle of incidence, is the angle to the normal, i.e. the line perpendicular to the surface, at the point of incidence. If a ray exits from a medium with a lower optical density and enters a medium with a higher optical density the angle of incidence becomes smaller, the ray is refracted and vice versa. Hereby, the values of the sines of the angles between the rays and the normal have a ratio equivalent to both refractive indices or the phase velocities.

${\sin \alpha \over \sin \beta }={v_{1} \over v_{2}}={n_{1} \over n_{2}}$

Light refraction

Light refraction occurs due to the variation of the velocity of light 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 vertical to the propagation direction. When these parallel lines strike a boundary surface at an angle, every point of incidence produces a new vibration, which propagates within the new material. However, because the velocity has changed, the wavelength and the distance between the parallels of the same amplitude changes, too. Due to the change in velocity, the propagation direction is also newly orientated.

As a means of simplification, only the parallel lines of the same amplitude are examined. 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. A new wavefront develops. Because 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 in dependance of the velocity within the first propagation medium, the wavefront in the second medium is differently orientated.

Diagrams missing!!