The refractive index of glass with respect to water is $9/8$ . If the velocity and wave length of light in glass are $2 \times 10^{8} m/s$ and $4000 A°$ respectively. Then the velocity and wavelength of light in water are

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2.25 \times 10^{8} m/s, 4500 A°

2.25 \times 10^{8} m/s, 5000 A°

3 \times 10^{8} m/s, 4500 A°

3 \times 10^{8} m/s, 5000 A°

answer is A.

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Detailed Solution

_{w} μ_{g} = \frac{9}{8} = \frac{μ_{g}}{μ_{w}}

$μ_{g} = 2 \times 10^{8} m/s, λ_{g} = 4000 {Å=4000×10}^{- 10} m$

$μ \propto \frac{1}{v} λ_{g} = 4 \times 10^{- 7} m$

$\frac{μ_{g}}{μ_{w}} = \frac{v_{g}}{v_{w}} \Rightarrow \frac{9}{8} = \frac{v_{w}}{2 \times 10^{8}} \Rightarrow v_{w} = \frac{18 \times 10^{8}}{8}$

$v_{w} = 2.25 \times 10^{8} m/s$

$μ α \frac{1}{λ}$

$\frac{μ_{g}}{μ_{w}} = \frac{λ_{w}}{μ_{g}} = \frac{9}{8}$

$λ_{w} = \frac{9}{8} \times 4 \times 10^{- 7} \Rightarrow λ_{w} = 4.5 \times 10^{- 7} m$

$λ_{w} = 4500 \times 10^{- 10} m$

$λ_{w} = 4500 Å$

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