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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