Refraction Of Light
REFRACTIVE INDEX:
I)Absolute refractive Index (µ):
The absolute refractive index of a medium is the ratio of speed of light in free space (C) to speed of light in a given medium (V).
µ=\(
\frac{{\text{velocity of light in free space (C)}}}
{{\text{ velocity of light in a given medium (V)}}}
\)
It is a scalar. It has no units and dimensions.
From electromagnetic theory if \(
\varepsilon _0
\) and \(
\mu _0
\) are the permittivity and permeability of free space, \(
\varepsilon
\) and µ are the permittivity and permeability of a given medium then refractive index of the given medium
\(
\mu = \frac{C}
{V} = \frac{{\frac{1}
{{\sqrt {\varepsilon _0 \mu _0 } }}}}
{{\frac{1}
{{\sqrt {\varepsilon \mu } }}}} = \sqrt {\frac{{\varepsilon \mu }}
{{\varepsilon _0 \mu _0 }}} = \sqrt {\varepsilon _r \mu _r }
\)
where \(
\varepsilon _r
\) & \(
\mu _r
\) are the relative permittivity and permeability of the given medium.
i) For vaccum or free space, speed of light of all wavelengths is same and is equal to C.
So, For all wavelengths the refractive index of free space is
\(
\mu = \frac{C}
{C} = 1
\)
ii) For a given medium the speed of light is different for different wavelengths, greater the wavelength of the light, greater will be the speed and hence lesser will be refractive index.
\(
\lambda _R > \lambda _v
\) , So in medium \(
\mu _v > \mu _R
\)
Note:
Actually refractive index \(
\mu
\) varies with \(
\lambda
\) according to the equation \(
\mu
\) = A+\(
\frac{B}
{{\lambda ^2 }}
\)
(Where A & B are constants)
iii) For a given light, denser the medium lesser will be the speed of light and so greater will be the refractive index.
Example: Glass is denser medium when compared to water, so \(
\mu _{glass} > \mu _{water}
\)
The refractive index of water \(
\mu _w
\)= 4/3
The refractive index of glass=\(
\mu _g
\)= 3/2
iv) For a given light and given medium, the refractive index is also equal to the ratio of wavelength of light in free space to that in the medium.
\(
\mu = \frac{C}
{V}
\) =\(
\left( {\frac{{f\lambda _{vaccum} }}
{{f\lambda _{medium} }}} \right) = \frac{{\lambda _{vaccum} }}
{{\lambda _{medium} }}
\)
(when light travells from vaccume to a medium, frequency does not change)
Note:
If C is velocity of light in free space \(
\lambda _0
\) is wavelength of given light in free space then velocity of light in a medium of refractive index ( µ) is \(
V_{medium}
\)=\(
\frac{C}
{\mu }
\).
Wave-length of given light in a medium of refractive index (µ) is \(
\lambda _{medium}
\)=\(
\frac{{\lambda _0 }}
{\mu }
\)
II) Relative Refractive Index:
When light passes from one medium to the other, the refractive index of medium 2 relative to medium 1 is written as and is given by
\(
{}_1\mu _2
\)=\(
\frac{{\mu _2 }}
{{\mu _1 }} = \frac{{v_1 }}
{{v_2 }} = \frac{{\lambda _1 }}
{{\lambda _2 }}
\)
refractive index of medium 1 relative to medium 2 is
\(
{}_2\mu _1
\) =\(
\frac{{\mu _1 }}
{{\mu _2 }} = \frac{{v_2 }}
{{v_1 }} = \frac{{\lambda _2 }}
{{\lambda _1 }}
\)
From eq. (1) & (2)\(
{}_1\mu _2
\) =\(
\frac{1}
{{2\mu _1 }}
\)
i.e., (\(
{}_1\mu _2
\)).(\(
{}_2\mu _1
\))=1