The absolute refractive indices of glass and water are 4/3 and 3/2 respectively. If the speed of light in glass is \[2\times {{10}^{8}}\,m/s,\] calculate the speed of light in |
(i) vacuum, (ii) water. |
Answer:
(i) Given : \[{{n}_{g}}=\frac{4}{3},\,\,{{n}_{w}}=\frac{3}{2},\,\,{{v}_{g}}=2\times {{10}^{8}}m/s\] We know that, \[{{n}_{g}}=\frac{c}{{{\upsilon }_{g}}}\] \[\therefore \] \[c={{n}_{g}}{{\upsilon }_{g}}\] \[=\frac{4}{3}\times 2\times {{10}^{8}}=2.67\times {{10}^{8}}m/s\] (ii) Also, \[{{n}_{w}}=\frac{c}{{{\upsilon }_{w}}}\] \[{{\upsilon }_{w}}=\frac{c}{{{n}_{w}}}=\frac{2.67\times 2\times {{10}^{8}}}{3}\] \[=1.78\times {{10}^{8}}\,m/s\]
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