Question

Light enters from air to glass having refractive index
1.50. What is the speed of light in the glass? The speed
of light in vacuum is 3 x 10⁸ ms-¹.​

Answer 1

GiveN :-

• Speed of light in vacuum is 3×10⁸ m/s.
• The RI of medium wrt vacuum is 1.4 .

To FinD :-

• The speed of light in that medium.

SolutioN :-

Given that Speed of light in vacuum is 3 x 10⁸m/s and the R.l. of glass with respect to vacuum is 1.5 and we need to find the speed of light in glass .

We know that the Refractive index is the ratio of speed of light in vacuum to the speed of light in a medium . So ,

★ According to Refractive Index :-

$\sf:\implies \pink{ \mu =\dfrac{ v_{(light \ in \ vaccum)}}{v_{(light \ in \ a \ med^m )}} }\\\\\sf:\implies 1.5 = \dfrac{3\times 10^8 m/s}{v }\\\\\sf:\implies v = \dfrac{3\times 10^8 m/s}{1.5}\\\\\sf:\implies\underset{\blue{\sf Required\ speed }}{\underbrace{ \boxed{\pink{\frak{ v_{(in \ glass)} = 2 \times 10^8 m/s }}}}}$

Answer 2

Given: Light enters from air to glass having refractive index 1.50 and speed of light in vacuum is 3 × 10⁸ ms⁻¹.

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Need to find: The speed of light in the glass.

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$\boldsymbol{\underline{\bigstar\;According\;to\;the\;formula\;:}}$

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• The index of refraction (μ) is the relation between the speed of light in a vacuum (c) and the speed of light in a substance (v).

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Therefore,

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$:\implies\sf{μ=\dfrac{\:c\:}{\:v\:}}\\\\\\:\implies\sf{1.5=\dfrac{3×10^8\;ms^{-1}}{v}}\\\\\\:\implies\sf{v=\dfrac{3×10^8\;ms^{-1}}{1.5}}\\\\\\:\implies{\underline{\boxed{\pink{\frak{v=2×10^8\;ms^{-1}}}}}}{\;\bigstar}$

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${\underline{\sf{Hence,\;the\;speed\;of\;light\;in\;the\;glass\;is\;\bf{2×10^8\;ms^{-1}}.}}}$