Question

The speed of light in air is 3 × 108 m/s and in glass it is 2 × 108m/s. What is the

refractive index of glass? If refractive index of diamond is 2.42 what is the

speed of light in the diamond?​

Answer 1

Given that :-

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• Speed of light in air = 3 × 10⁸ m/s

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• Speed of light in glass = 2 × 10⁸ m/s

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• Refractive index of diamond = 2.24

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To Find :-

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• Refractive index of glass = ??

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• Speed of light in diamond = ??

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Concept use :-

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What is refractive index ?

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Refractive index is defined as the ratio of the speed of light in vacuum to the speed of light in that medium .

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$\sf \boxed{\mu = \dfrac{ Speed \: of \: light\: in \: vacuum }{ Speed\: of\: light \: in \: that\: medium}}$

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Solution :-

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We know that speed of light in vacuum is equal to the speed of light in air

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Therefore ;

Speed of light in vacuum = 3 × 10⁸ m/s

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From the formulae :-

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$\sf \boxed{\mu = \dfrac{ Speed \: of \: light\: in \: vacuum }{ Speed\: of\: light \: in \: that\: medium}}$

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Where ;

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μ = Refractive index

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We get that ;

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$\sf {\mu = \dfrac{ 3 \times 10^8 }{ 2\times 10^8}}$

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$\sf {\mu = \dfrac{ 3 }{ 2 }}$

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$\sf {\mu = 1.5 }$

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Therefore ; Refractive Index of glass is 1.5

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Now ; Given that

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$\sf {2.42 = \dfrac{ Speed \: of \: light\: in \: vacuum }{ Speed\: of\: light \: in \: diamond }}$

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$\sf {2.42 = \dfrac{ 3 \times 10^8 }{ Speed\: of\: light \: in \: diamond }}$

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$\sf {Speed \: of \: light\: in\: diamond = \dfrac{3\times 10^8}{2.42}}$

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$\sf {Speed \: of \: light\: in\: diamond = \dfrac{1\times 10^8}{0.8}}$

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$\sf {Speed \: of \: light\: in\: diamond = \dfrac{10\times 10^8}{8}}$

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$\sf {Speed \: of \: light\: in\: diamond = \dfrac{5\times 10^8}{4}}$

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$\sf {Speed \: of \: light\: in\: diamond = \dfrac{1.25\times 10^8}{1}}$

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$\sf {Speed \: of \: light\: in\: diamond = 1.25\times 10^8 m/s ( approx ) }$

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Speed of light in diamond is 1.25 × 10⁸ m/s approx .

Answer 2

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

• Speed of light in air = 3×10⁸ m/sec

• Speed of light in glass = 2×10⁸ m/sec

• Refractive index of diamond = 2.42

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

• Refractive index of glass.

• Speed of light in diamond.

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

$\small \boxed{ \sf{refractive \: index( \mu )= \frac{speed \: of \: light \: in \: air}{speed \: of \: light \: in \: given \: medium} }}$

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

$\sf{ \mu_{ (glass)} = \frac{speed \: of \: light \: in \: air}{speed \: of \: light \: in \: glass} } \\ \\ \\ \sf{ \mu_{(glass)} = \frac{3 \times {10}^{8} }{2 \times {10}^{8} } } \\ \\ \\ \boxed{ \sf{ \pink{\mu_{(glass)} = 1 .5}}}$

$\\ </p><p> \boxed{\sf{ \mu_{(diamond)} = \frac{speed \: of \: light \: in \: air}{speed \: of \: light \: in \: diamond} }}$

$\\ \\ \sf{2.41 = \frac{3 \times {10}^{8} }{speed \: of \: light \: in \: diamond} } \\ \\ \\ \sf{speed \: of \: light \: in \:diamond = \frac{3 \times {10}^{8} }{2.41} } \\ \\ \\ \small\boxed{ \sf{ \pink{speed \: of \: light \: in \: diamond = 1.24 \times {10}^{8} \frac{m}{sec} }}}$

More to know :-

• Refractive index is unitless quantity.

• More the refractive index of medium , less is speed of light in that medium.

• Diamond had highest Refractive index.