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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 (μ) = \(\frac{c(speed\,of\,light\,in\,vaccum)}{v(speed\,of\,light\,in\,any\,medium)}\)

Given μ = 2.42, c = 3 × 108.

Putting the value in the above formula, we get

⇒ 2.42 = \(\frac{3\,\times\,10^8}{v}\)

⇒ v = \(\frac{3\,\times\,10^8}{2.42}\)

⇒ v = 1.23 × 108 m/s.

Speed of light in diamond is 1.23 × 108 m/s

% of speed in diamond = \(\frac{1.23\,\times\,10^8}{3\,\times\,10^8}\)x 100 = 0.41 x 100 = 41%

Thus there is 41% decrease in the speed of light in diamond than in air.

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