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The index of refraction is defined as the ratio of the sped of light in a vacuum to the speed of light in the meduiu of interest, in the is case diamond. So n=c/v, n= index, c=speed of light and v= speed of light in diamond. 2.42=c/v so v=c/2.42, c≈3x108 m/sec so v=1.24x108 m/sec.
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Refractive index=speed of light in air/speed of light in media
=>2.47=3*10 ^8/x
=>speed of light in diamond =3*10^8 /2.47
=1.21×10^8m/s
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