\section{REFRACTION AT PLANE SURFACES}

\section{Introduction :}

The phenomenon of change in path of light as it goes from one medium to another is called refraction.

Refraction phenomenon can be categories, depending upon the type of separating surface which can be further subdivided depending upon the shape of the medium as follows :


Absolute Refractive Index :

The refractive index of a medium is defined as the ratio of the speed of light in vacuum (c) to the speed of light in the medium (v), i.e., \(n=c / v\)

(i) It is a scalar quantity without any unit or dimension.

(ii) If \(\varepsilon_{0}\) and \(\mu_{0}\) are electric permittivity and magnetic permeability of vacuum while \(\varepsilon\) and \(\mu\) are that of a given medium then,

\[

c=\frac{1}{\sqrt{\varepsilon_{0} \mu_{0}}} \quad \text { and } \quad v=\frac{1}{\sqrt{\varepsilon \mu}}

\]

so that\( (n=\frac{\mathrm{c}}{\mathrm{v}}=\sqrt{\frac{\varepsilon \mu}{\varepsilon_{0} \mu_{0}}}=\sqrt{\varepsilon_{r} \mu_{r}} \)

(iii) For vacuum, \(n=1\) as \(v=c\)

(iv) Absolute refractive index of any medium is greater than one.

(v) Refractive index of a medium also depends on the wavelength of light used. As per Cauchy's formula

\( n=A+B / \lambda^{2}+\ldots . \)

"longer the wavelength smaller is the refractive index". 

Relative Refractive Index:

The relative refractive index of two media is equal to the ratio of their absolute refractive indices.

\[

\( \begin{aligned} & \therefore \quad{ }_{1} \mathrm{n}_{2}=\frac{\mathrm{n}_{2}}{\mathrm{n}_{1}}=\frac{\mathrm{c} / \mathrm{v}_{2}}{\mathrm{c} / \mathrm{v}_{1}}=\frac{v_{1}}{v_{2}} \\ &=\frac{\text { Velocity of light in first medium }}{\text { Velocity of light in sec ond medium }} \end{aligned} \)

\( \begin{gathered} { }_{2} \mathrm{n}_{1}=\frac{\mathrm{n}_{1}}{\mathrm{n}_{2}}=\frac{v_{2}}{v_{1}} \\ \Rightarrow \quad{ }_{1} \mathrm{n}_{2} \times{ }_{2} \mathrm{n}_{1}=\frac{v_{1}}{v_{2}} \times \frac{v_{2}}{v_{1}}=1 \\ \therefore \quad{ }_{1} \mathrm{n}_{2}=\frac{1}{{ }_{2} \mathrm{n}_{1}} \end{gathered} \] \)

(a) Frequency (and hence colour) and phase do not change (while wavelength and velocity changes)

(b) Incident ray, refracted ray, and normal always lie in the same plane.

(c) Snell's Law :

Ratio of Sine of angle of incidence to Sine of angle of refraction is always a constant, i.e., for all values of i \& \(\mathrm{r}\) -

\( \begin{aligned} \frac{\sin \mathrm{i}}{\sin \mathrm{r}}=\text { Constant } & ={ }_{1} \mathrm{n}_{2} \\ & =\frac{\text { Velocity of light in first medium }}{\text { Velocity of light in second medium }} \end{aligned}   \)

\[

\frac{\sin \mathrm{i}}{\sin \mathrm{r}}=\frac{v_{1}}{v_{2}}=\frac{\lambda_{1}}{\lambda_{2}}

\]

where \({ }_{1} \mathrm{n}_{2}\) is Refractive index of medium-2 w.r.t. Medium-1.