Question

The index of refraction of fused quartz is 1⋅472 for light of wavelength 400 nm and is 1⋅452 for light of wavelength 760 nm. Find the speeds of light of these wavelengths in fused quartz.

Answer 1

Given:
Refractive index of fused quartz for light of wavelength 400 nm is 1.472.
And refractive index of fused quartz for light of wavelength 760 nm is 1.452.
We known that refractive index of a material is given by
μ = $\frac{\mathrm{Speed}\mathrm{of}\mathrm{light}\mathrm{in}\mathrm{vacuum}}{\mathrm{Speed}\mathrm{of}\mathrm{light}\mathrm{in}\mathrm{the}\mathrm{material}}=\frac{c}{v}$
Let speed of light for wavelength 400 nm in quartz be v₄₀₀.
So,
$$\begin{gathered} 1.472=\frac{3\times {10}^8}{v_{400}} \\ \Rightarrow v_{400}=2.04\times {10}^8\mathrm{m}/\mathrm{s} \end{gathered}$$
Let speed of light of wavelength 760 nm in quartz be v₇₆₀.
Again, $\frac{1.452}{1}=\frac{3\times {10}^8}{{\nu }_{760}}$
$\Rightarrow v_{760}=2.07\times {10}^8\mathrm{m}/\mathrm{s}$