The refractive index of fused quartz is 1.46 and that of sapphire is 1

The refractive index of fused quartz is 1.46 and that of sapphire is 1.77. If v_q is the speed of light in quartz and v_s is the speed of light in sapphire, then which one of the following relations is correct ?

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”v<sub>q</sub>

”v<sub>s</sub>

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This question was previously asked in

UPSC NDA-2 – 2020

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The relation v_q > v_s is correct.

The refractive index (n) of a medium is inversely proportional to the speed of light (v) in that medium, according to the formula n = c/v, where c is the speed of light in a vacuum. Therefore, v = c/n. A higher refractive index means a lower speed of light, and a lower refractive index means a higher speed of light.

Given n_q = 1.46 and n_s = 1.77. Since n_s > n_q, it follows that v_s = c/n_s must be less than v_q = c/n_q. Hence, v_q > v_s. The speed of light is slower in sapphire than in fused quartz because sapphire has a higher refractive index.

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