Question

The speed of light in air is 3 x 10°m/s and that in diamond is 14 x 108m/s. Find refractive index
of diamond​

Answer 1

• Speed of light in air , c = 3 × 10⁸ m/s

• Speed of light in diamond, v = 1.24 × 10⁸ m/s

Refractive index of diamond, μ

μ = c/v

$= \dfrac{3 \times {10}^{8} }{1.24 \times {10}^{8} } \\ \\ = \dfrac{3}{1.24} \\ \\ = \dfrac{3}{1.24} \times \frac{100}{100} \\ \\ = \dfrac{3 \times 100}{1.24 \times 100} \\ \\ = \dfrac{300}{124} \\ \\ = \frac{150}{62} \\ \\ = \frac{75}{31} \\ \\ \mu = 2.42$

Refractive index of diamond is 2.42

• Since refractive index is a ratio of two similar quantities , it has no unit.

• It is unitless and dimensionless.

• Refractive index is inversely proportional to the velocity of light in that medium.

• Light travels faster in the medium with lower refractive index.

Answer 2

$\\ \large\underline{ \underline{ \sf{ \red{correct \:question :} }}}$

• The speed of light in air is 3×10⁸ m/sec and that of diamond is 1.24×10⁸ m/sec . Find refractive index of diamond.

$\large\underline{ \underline{ \sf{ \red{given :} }}}$

• Speed of light = 3 × 10⁸ m/sec

• Speed of diamond = 1.24 × 10⁸ m/sec

$\\ \\ \large\underline{ \underline{ \sf{ \red{to \: find :} }}}$

• Refractive index of Diamond.

$\\ \\ \large \sf\underline{ \underline{ \red{to \: know : }}} \\ \\ \boxed{ \tiny{\sf{refractive \: index( \mu) = \frac{speed \: of \: light \: in \: vacuum \: or \: air}{speed \: of \: light \: in \:given \: medium } }}}$

$\\ \\ \large\underline{ \underline{ \sf{ \red{solution:} }}}$

Putting values , we get..

$\\ \sf{ \mu = \frac{3 \times {10}^{8} }{1.24 \times {10}^{8} } } \\ \\ \\ \sf{ \mu = \frac{3}{1.24} } \\ \\ \\ \boxed{ \sf{ \pink{ \mu = 2.41}}}$

Hence , refractive index of diamond is 2.41.

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More to know :-

• Refractive index is unitless quantity.

• Refractive index of a medium is inversely proportional to its speed of light in that medium.

• Diamond has maximum refractive index.