Refractive index of water with respect to air is 1.33 and that of diamond is 2.42.
(i) In which medium does the light move faster, water or diamond?
(ii) What is the refractive index of diamond with respect to water?
(A) We Know that Refractive index of a medium is equal to the ratio of the speed of light in that vacuum to the speed of light in that medium. So, the more the value of the refractive index is less, the speed of light in that medium. Thus, in water light moves faster.
(B) Given us, refractive index of water with respect to air is 1.33
and the refractive index of diamond with respect to air is 2.4
We need to find the refractive index of diamond with respect to water.
We know that, Refractive index = `"Speed of light in vacuum"/"Speed of light in medium"`
Since the refractive index of diamond is more, hence the speed of light is lesser in diamond.
Let speed of light in water vevw and in diamond be `"V"_"d"`
Refractive index of diamond w.r.t water is say n = `"Speed of light in vacuum"/"Speed of light in Diamond"`
n = `\frac{V_{w}}{V_{d}}`
Now,
Dividing both numerator and denominator by speed of light [c] we get
n = `\frac{\frac{V_{w}}{C}}{\frac{V_{d}}{C}}`
`\therefore` Inverse Ratio of refractive index of water and diamond.
n = `\frac{2.42}{1.33}` = 1.82
Thus, 1.82 is the refractive index of diamond with respect to water.
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