Light as a Wave

Light is an electromagnetic wave

• Light waves are TRANSVERSE. They consist of tiny oscillating electric and magnetic fields which are perpendicular to each other and perpendicular to the direction of propagation.
• They require no material medium and travel even through vacuum, at $c=3\times10^{8}$ m/s.
• The speed $v$ in a material medium depends on the refractive index $n$ of the medium, which in turn depends on the permeability and permittivity of the medium.

$$n=\dfrac{c}{v}$$

The refractive index is the ratio of the speed of light in vacuum to the speed of light in the medium. For vacuum $n=1$; for air $n$ may be taken as 1.

The electromagnetic spectrum

Electromagnetic waves range in wavelength from less than a femtometre ($10^{-15}$ m) to more than a kilometre. In INCREASING order of wavelength they are classified as:

• gamma rays, X-rays, ultraviolet, visible, infrared, microwave, radio waves.

Visible light occupies $400$ nm to $700$ nm. Different wavelengths in this range are perceived as different colours, violet having the shortest and red the longest wavelength. White light is a mixture of waves of many wavelengths.

Why white light disperses

The refractive index of a medium depends on the wavelength of the incident light. Hence for the same angle of incidence the angle of refraction is different for different colours (except at normal incidence, where all colours go straight through). The colours present in white light therefore separate on passing through a transparent medium — this is the reason for the formation of a spectrum by a prism, and for the rainbow.

Working relations

$$c=\nu\lambda_{0},\qquad v=\nu\lambda_{m},\qquad \lambda_{m}=\dfrac{\lambda_{0}}{n}$$

$$\bar{\nu}=\dfrac{1}{\lambda}\ \ (\text{wave number, }\text{m}^{-1})$$

$$_{1}n_{2}=\dfrac{n_{2}}{n_{1}}=\dfrac{v_{1}}{v_{2}}=\dfrac{\lambda_{1}}{\lambda_{2}}$$

Standard results

• $n=\dfrac{c}{v}$; larger $n$ means slower light and shorter wavelength.
• The frequency of a light wave is fixed by the source and never changes on refraction.
• $_{w}n_{g}=\dfrac{_{a}n_{g}}{_{a}n_{w}}$ — combine absolute indices this way for "glass with respect to water" questions.
• Speed of light is independent of the motion of the source or the observer, and nothing can exceed it in vacuum.