A ray of light enters a diamond from air. If the refractive index of diamond is 2.42, what % (percentage) is speed of light in diamond with that of speed in air?
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Refractive index $(\mu)=\frac{\text{c (speed of light in vaccum)}}{\text{v (speed of light in any medium)}}$Given $\mu=2.42,\text{c}=3\times10^8.$
Putting the value in the above formula, we get$\Rightarrow2.42=\frac{3\times10^8}{\text{v}}$
$\Rightarrow\text{v}=\frac{3\times10^8}{2.42}$
$\Rightarrow\text{v}=1.23\times10^8\text{m/s.}$
Speed of light in diamond is $1.23\times10^8\text{m/s}$ % of speed in diamond $=\frac{1.23\times10^8}{3\times10^8}\times100=0.41\times100=41\%$ Thus there is 41% decrease in the speed of light in diamond than in air.
Putting the value in the above formula, we get$\Rightarrow2.42=\frac{3\times10^8}{\text{v}}$
$\Rightarrow\text{v}=\frac{3\times10^8}{2.42}$
$\Rightarrow\text{v}=1.23\times10^8\text{m/s.}$
Speed of light in diamond is $1.23\times10^8\text{m/s}$ % of speed in diamond $=\frac{1.23\times10^8}{3\times10^8}\times100=0.41\times100=41\%$ Thus there is 41% decrease in the speed of light in diamond than in air.
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