Express the refractive index of Medium 2 with respect to Medium 1 in terms of the speed of light in both media.
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The refractive index \( n \) is the ratio of the speed of light in a vacuum to the speed of light in the medium, and it determines how much light bends when passing through the medium.
The refractive index \( n \) of a substance is defined as the ratio of the speed of light in a vacuum \( c \) to the speed of light in that substance \( v \):\[n = \frac{c}{v}\]Here, \( c \) represents the speed of light in a vacuum, and \( v \) represents the speed of light within the substance. The refractive index of Medium 2 relative to Medium 1 is:\[n_{21} = \frac{v_1}{v_2}\]where \( v_1 \) is the speed of light in Medium 1 and \( v_2 \) is the speed of light in Medium 2.Therefore, the refractive index of Medium 2 with respect to Medium 1 is \( n_{21} = \frac{v_1}{v_2} \).
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