The refractive index of glass with respect to water is 9/8. If the velocity and wavelength of light in water are 2.25×10⁸ m/s and 5400 A⁰ respectively find the velocity and wavelength of light in glass

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$2.0 \times 10^{8} m / s, 4800 A^{0}$

$2.0 \times 10^{8} m / s, 6075 A^{0}$

$1.0 \times 10^{8} m / s, 4800 A^{0}$

$1.0 \times 10^{8} m / s, 6075 A^{0}$

answer is A.

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Detailed Solution

$\frac{μ_{g}}{μ_{w}} = \frac{9}{8}; μ \propto \frac{1}{V}, \frac{μ_{g}}{μ_{w}} = \frac{V_{w}}{V_{g}}; \frac{μ_{g}}{μ_{w}} = \frac{λ_{w}}{λ_{g}}$

$\Rightarrow V_{g} = V_{w} \times \frac{μ_{w}}{μ_{g}} = 2.0 \times 10^{8} m / s$

$\Rightarrow λ_{g} = λ_{w} \times \frac{μ_{w}}{μ_{g}} = 4800 \overset{0}{A}$

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