question_answer

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, \[{{n}_{w}}=\frac{c}{{{\upsilon }_{w}}}\]

\[{{\upsilon }_{w}}=\frac{c}{{{n}_{w}}}=\frac{2.67\times 2\times {{10}^{8}}}{3}\]

\[=1.78\times {{10}^{8}}\,m/s\]