# JEE Main & Advanced Physics Ray Optics Refractive Index

Refractive Index

Category : JEE Main & Advanced

(1) Refractive index of a medium is that characteristic which decides speed of light in it.

(2) It is a scalar, unit less and dimensionless quantity.

(3) Absolute refractive index : When light travels from vacuum to any transparent medium then refractive index of medium w.r.t. vacuum is called it's absolute refractive index i.e. $_{\text{vacuum}}{{\mu }_{\text{medium}}}=\frac{c}{v}$

Absolute refractive indices for glass, water and diamond are respectively ${{\mu }_{g}}=\frac{3}{2}=1.5,\,{{\mu }_{w}}=\frac{4}{3}=1.33\,\text{and }{{\mu }_{\text{D}}}=\frac{12}{5}=2.4$

(4) Relative refractive index : When light travels from medium (1) to medium (2) then refractive index of medium (2) w.r.t. medium (1) is called it's relative refractive index i.e. $_{1}{{\mu }_{2}}=\frac{{{\mu }_{2}}}{{{\mu }_{1}}}=\frac{{{v}_{1}}}{{{v}_{2}}}$ (where ${{v}_{1}}$ and ${{v}_{2}}$ are the speed of light in medium 1 and 2 respectively).

(5) When we say refractive index we mean absolute refractive index.

(6) The minimum value of absolute refractive index is 1. For air it is very near to 1. $(\tilde{=}1.003)$

(7) Cauchy's equation : $\mu =A+\frac{B}{{{\lambda }^{2}}}+\frac{C}{{{\lambda }^{4}}}+......$

$({{\lambda }_{\text{Red}}}>{{\lambda }_{\text{violet}}}$so ${{\mu }_{\text{Red}}}<{{\mu }_{\text{violet}}})$

(8) If a light ray travels from medium (1) to medium (2), then

$_{1}{{\mu }_{2}}=\frac{{{\mu }_{2}}}{{{\mu }_{1}}}=\frac{{{\lambda }_{1}}}{{{\lambda }_{2}}}=\frac{{{v}_{1}}}{{{v}_{2}}}$

(9) Dependence of Refractive index

(i) Nature of the media of incidence and refraction.

(ii) Colour of light or wavelength of light.

(iii) Temperature of the media : Refractive index decreases with the increase in temperature.

Indices of refraction for various substances, Measured with light of vacuum wavelength ${{\lambda }_{0}}=589\,\,nm$

 Substance Refractive index Substance Refractive index Solids at ${{20}^{o}}C$ Liquids at ${{20}^{o}}C$ Diamond (C) 2.419 Benzene 1.501 Fluorite $(Ca{{F}_{2}})$ 1.434 Carbon disulfide 1.628 Flused quartz $(Si{{O}_{2}})$ 1.458 Carbon tetrachloride 1.461 Glass, crown 1.52 Ethyl alcohol 1.361 Glass, flint 1.66 Glycerine 1.473 Ice $({{H}_{2}}O)$ (at ${{0}^{o}}C$) 1.309 Water 1.333 Polystyrene 1.49 Gases at ${{0}^{o}}C$, 1 atm Sodium chloride 1.544 Air 1.000293 Zircon 1.923 Carbon dioxide 1.00045

(10) Reversibility of light and refraction through several media

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