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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