Find the speed of light in a transparent medium if the refractive index of the medium is $1.8$ ?

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Solution

Step-1:Given
Refractive index of the medium, $n = 1.8$
Consider, Speed of the light in the vacuum, $c = 3 \times 10^{8} \frac{m}{s}$
Step-2: Formula
Refractive index, $n = \frac{S p e e d o f l i g h t i n v a c u u m (c)}{S p e e d o f l i g h t i n a n y m e d i u m (ν)}$
Step-3: Speed of light in the transparent medium
$S p e e d o f l i g h t i n a n y m e d i u m (ν) = \frac{S p e e d o f l i g h t i n a i r (c)}{n} \Rightarrow ν = \frac{3 \times 10^{8} \frac{m}{s}}{1.8} \Rightarrow ν = 1.66 \times 10^{8} \frac{m}{s}$
Hence, the speed of light in the transparent medium is $ν = 1.66 \times 10^{8} \frac{m}{s}$

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