state the laws of refraction of light.explain the term absolute refractive index of a medium and write an expression to relate it with speed of light in vacuum.
Answers
The law of refraction, which is generally known as Snell's law, governs the behaviour of light-rays as they propagate across a sharp interface between two transparent dielectric media.
Consider a light-ray incident on a plane interface between two transparent dielectric media, labelled 1 and 2, as shown in Fig. 57. The law of refraction states that the incident ray, the refracted ray, and the normal to the interface, all lie in the same plane. Furthermore,
\begin{displaymath} n_1\,\sin\theta_1 = n_2\,\sin\theta_2, \end{displaymath}
where $\theta_1$ is the angle subtended between the incident ray and the normal to the interface, and $\theta_2$ is the angle subtended between the refracted ray and the normal to the interface. The quantities $n_1$ and $n_2$ are termed the refractive indices of media 1 and 2, respectively. Thus, the law of refraction predicts that a light-ray always deviates more towards the normal in the optically denser medium: i.e., the medium with the higher refractive index. Note that $n_2>n_1$ in the figure. The law of refraction also holds for non-planar interfaces, provided that the normal to the interface at any given point is understood to be the normal to the local tangent plane of the interface at that point.
Figure 57: The law of refraction. \begin{figure} \epsfysize =3in \centerline{\epsffile{refract.eps}} \end{figure}
The absolute refractive index is defined as a ratio of the speed of light in vacuum and in selected medium. Generally, the refractive index depends on the wavelength of incident light. Relative refractive index is defined as a ratio of speeds of light in two different media.
Mathematically refractive index [\eta]\ =\frac{v_{1}} { v_{2}}
v_{1} is the velocity of light in first medium.
v_{2} is the velocity of light in second medium i.e the medium under consideration.
Let the first medium is space or vacuum.
Now, the velocity of light in first medium will be c where c is the velocity of light.
Now, the refractive index \eta\ =\frac{c}{v}
v is the velocity of light in second medium i.e medium under consideration.
Now the refractive index obtained is called absolute refractive index.
Hence, the absolute refractive index of a medium is defined as the ratio of the velocity of light in air to the velocity of light in that medium.
Mathematically the absolute refractive index =
\eta\ =\frac{velocity\ of\ in\ light\ air}{velocity\ of\ light\ in\ medium}