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.

Q: 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.

1. $\text{n}_{g} = \frac{4}{3};$ $\text{n}_{w} = \frac{3}{2};$ $\text{v}_{g} = 2\times10^{8}\text{m/s}$ $\text{n}_{g} = \frac{\text{C}}{\text{v}_{g}}$ $\therefore\text{c} = \text{n}_{g}\text{v}_{g} =\frac{4}{3}\times2\times10^{8}\text{m/s} = 2.67\times10^{8}\text{m/s}$ 2. $\text{n}_{w} = \frac{\text{C}}{\text{V}_{w}}$ $\therefore\text{V}_{w} =\frac{\text{C}}{\text{n}_{w}} =\frac{2.67\times2\times10^{8}}{3} = 1.78\times10^{8}\text{m/s}.$

Question

CBSE OUTSIDE DELHI - SET 1 2015

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Solution

$\text{n}_{g} = \frac{4}{3};$

$\text{n}_{w} = \frac{3}{2};$

$\text{v}_{g} = 2\times10^{8}\text{m/s}$

$\text{n}_{g} = \frac{\text{C}}{\text{v}_{g}}$

$\therefore\text{c} = \text{n}_{g}\text{v}_{g} =\frac{4}{3}\times2\times10^{8}\text{m/s} = 2.67\times10^{8}\text{m/s}$

$\text{n}_{w} = \frac{\text{C}}{\text{V}_{w}}$

$\therefore\text{V}_{w} =\frac{\text{C}}{\text{n}_{w}} =\frac{2.67\times2\times10^{8}}{3} = 1.78\times10^{8}\text{m/s}.$

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