If the speed of light in carbon disulfide and vacuum is X and Y respectively, then
- (a)X < Y
- (b)X > Y
- (c)X ≥ Y
- (d)X = Y
Correct — A, X < Y. Light travels fastest in vacuum, at c ≈ 3 × 10⁸ m/s; in any transparent medium it slows to v = c/n, where n is the refractive index. Carbon disulfide is optically dense, with n ≈ 1.63, so its speed of light X is about c/1.63, well below the vacuum speed Y. Hence X < Y.
- (b)X > Y — Nothing travels faster than light in vacuum; light cannot be quicker inside a medium than in free space, so X cannot exceed Y.
- (c)X ≥ Y — This allows X to equal or exceed Y; both are impossible for a medium with refractive index greater than 1.
- (d)X = Y — The speeds would be equal only if the refractive index were exactly 1 (vacuum, or effectively air); carbon disulfide has n ≈ 1.63, so the speeds differ.
The refractive index of a medium is n = c/v, the ratio of the speed of light in vacuum to its speed in the medium. Because every transparent material has n greater than 1, light always travels slower in a medium than in vacuum. The larger the refractive index, the slower the light and the more it bends on entering.
The question hides a simple rule behind an unfamiliar liquid. You do not need the exact value of carbon disulfide's index — just the principle that light in any medium is slower than in vacuum, so X < Y.
- Speed of light in vacuum c ≈ 3 × 10⁸ m/s is the universal upper limit; nothing carries information faster.
- In a medium the speed is v = c/n, so v < c whenever n > 1.
- Carbon disulfide is a highly refractive liquid with n ≈ 1.63, giving a notably slow light speed.
- A higher refractive index means slower light and greater bending — the basis of prisms and lenses.
- Thinking light can move faster inside a medium than in vacuum — it never does.
- Assuming the answer needs the exact refractive index; the principle v < c is enough.
Asked by comparing the speed of light in two media, or by linking refractive index to how much light slows and bends.
Assertion (A): A diamond sparkles more than a glass imitation cut to the same shape. Reason (R): The refractive index of diamond is less than that of glass. In the context of the above two statements, which one of the following is correct?
- (a) Both A and R are true, and R is the correct explanation of A
- (b) Both A and R are true, but R is not a correct explanation of A
- (c) A is true, but R is false
- (d) A is false, but R is true
Answer(c) A is true, but R is false
Same concept — refractive index and its effect on light. That UPSC item turns on diamond's high refractive index (which the Reason wrongly calls low); this NDA one uses the same idea that a higher index means light travels more slowly in the medium.
- practice — not a real PYQ
Light travels slowest in which one of the following media (highest refractive index)?
- (a)Vacuum
- (b)Air
- (c)Water
- (d)Diamond
Answer(d) Diamond — with n ≈ 2.42 it has the highest index here, so light slows the most in it.
- practice — not a real PYQ
If the refractive index of a medium is 1.5, the speed of light in it is about
- (a)3 × 10⁸ m/s
- (b)2 × 10⁸ m/s
- (c)4.5 × 10⁸ m/s
- (d)1.5 × 10⁸ m/s
Answer(b) 2 × 10⁸ m/s — v = c/n = (3 × 10⁸)/1.5.