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Question 38

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason(R).
Assertion (A) :
Refractive index of glass is higher than that of air.
Reason (R) : Optical density of a medium is directly proportionate to its mass density which results in a proportionate refractive index.
In the light of the above statements, choose the most appropriate answer from the options given below :

The assertion states: “Refractive index of glass is higher than that of air.”
The refractive index $$n$$ of a medium is defined by $$n = \frac{c}{v}$$, where $$c$$ is the speed of light in vacuum and $$v$$ is the speed of light in the medium. For air, $$v$$ is almost equal to $$c$$, so $$n_{\text{air}}\approx 1.0003$$. For ordinary crown glass, $$v\approx 2\times 10^{8}\,\text{m s}^{-1}$$, so $$n_{\text{glass}}\approx 1.5$$. Hence $$n_{\text{glass}}\gt n_{\text{air}}$$, making the assertion true.

The reason claims: “Optical density of a medium is directly proportionate to its mass density which results in a proportionate refractive index.”
Optical density describes how much a medium slows light, i.e. its refractive index. Mass density is the ratio of mass to volume. There is no fixed proportionality between mass density and refractive index. For example, turpentine has a higher refractive index than water even though its mass density is lower. Therefore the reason is false.

Conclusion: The assertion (A) is correct, but the reason (R) is not correct.
Hence the appropriate choice is Option C.

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