General properties of light

Reflection


The first property of light we consider is reflection from a surface, such as that of a mirror.

when light is reflected, qI = qR.
When light is reflected off any surface, the angle of incidence ( qI ) is always equal to the angle of reflection ( qR ).

Note:

The angles are always measured relative to the normal to the surface.
The law of reflection is also consistent with the particle picture of light.

Refraction


Refraction is the bending of light as it passes between materials of different density.
The index of refraction of a material is the ratio of the speed of light in vacuum to the speed of light in that material:

n =c/v


where v is the speed of light in the material.

Note:

The more dense the material, the slower the speed of light in that material. Thus n > 1 for all materials, and increases with increasing density. n = 1 in vacuum.

The frequency of light does not change when it passes from one medium to another. According to the formula v = l f , the wavelength must change. The index of refraction can therefore be written in terms of wavelengths as:

n =l0/l

where l0 is the wavelength of the light in the vacuum and l is the wavelength of the light in the medium.

Explanation for Refraction of Light

The change in speed and wavelength at the boundary between two materials causes light to change direction. Think of a car approaching a patch of mud at a sharp angle from a well paved road. The tire that hits the mud first will slow down, while the other tire is still going fast on the good road. This will cause the car to turn, until both tires are in the mud and going at the same speed. If q1 is the angle of the ray relative to the normal to the surface in medium 1, and q2 is the angle relative to the normal in medium 2, then 

sin q1   l1   n1   v1
————— = —— = —— = ——
sin q2   l2   n2   v2
Where v1 and l1 are the speed and wavelength in medium 1, etc.

Refraction between two substances, n1 being more dense.

Note:

This relationship between the angles is called Snell's Law.
The relation between the two angles is the same whether the ray is moving from medium 1 to 2 (so that q1 is the angle of incidence and q2 is the angle of refraction) or whether the ray moves from medium 2 to medium 1, so that q2 is the angle of incidence and q1 is the angle of refraction.
Total Internal Reflection
For a light ray passing from a more dense to a less dense material, there is a critical angle of incidence qc for which the angle of refraction is 90°. For greater angles of incidence, the light cannot pass through the boundary between the materials, and is reflected within the more dense material. For a light ray trying to pass from medium 2 to medium 1, the critical angle is given by:

sin qc = n1/n2 sin 90°= n1/n2

where n1 is the index of refraction of the less dense material, and n2 is the index of refraction of the more dense material.

Note:

The formula for the critical angle shows that n2 must be greater than n1 for there to be total internal reflection. That is, medium 2 must be denser than medium 1. Otherwise sin qc > 1, which is not possible.

Dispersion


The velocity of light in a material, and hence its index of refraction, depends on the wavelength of the light. In general, n varies inversely with wavelength: it is greater for shorter wavelengths. This causes light inside materials to be refracted by different amounts according to the wavelength (or colour). This gives rise to the colours seen through a prism. Rainbows are caused by a combination of dispersion inside the raindrop and total internal reflection of light from the back of raindrops. The following is a chart giving 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

Variations of index of refraction in glass

Diffraction


Diffraction is the apparent "bending" of light waves around obstacles in its path.

Diffraction through a slit

This bending is due to Huygen's principle, which states that all points along a wave front act as if they were point sources. Thus, when a wave comes against a barrier with a small opening, all but one of the effective point sources are blocked, and the light coming through the opening behaves as a single point source, so that the light emerges in all directions, instead of just passing straight through the slit.

Note:

For sizeable diffraction effects to occur the width of the opening must be of the same order or less than the wavelength of the light used.
Diffraction limits the resolving power of microscopes and other magnifying devices. If the object being viewed is smaller than the wavelength of light used, then the light diffracts around the object, and severely distorts the image. Thus microscopes using visible light have a resolving power of only about 600 nm » 10- 6m, but X-rays, whose wavelength is about 0.1 nm ( 10- 10 m) have a resolving power four orders of magnitude smaller.
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