Question

The speed of light in air is 3x 108ms-. If refractive index
of diamond is 2.42 then find the speed of light in it.

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Answer 1

Need To FinD :-

• The speed of light in diamond

$\red{\frak{ Given}}\begin{cases} \textsf{ Speed of light is 3 \times 10 ^{\sf 8} m/s .}\\\textsf{ The refractive index of diamond is 2.42 .}\end{cases}$

We know that the refractive index is defined as the speed to light in vacuum to the speed of light in any medium . Using this we have ,

$\sf:\implies \pink{ \mu = \dfrac{Speed _{(of \ light \ in \ vacuum )} }{Speed _{(of \ light \ in \ med^m)} } }\\\\\sf:\implies 2.42 = \dfrac{ 3 \times 10^8 m/s }{v_{(Diamond)} }\\\\\sf:\implies v_{(Diamond)}= \dfrac{3 \times 10^8 m/s}{2.42 } \\\\\sf:\implies\underset{\blue{\sf Required \ Speed }}{\underbrace{\boxed{\pink{\frak{ Speed_{(Diamond)}= 1.23 \times 10^8 m/s}}}}}$