The refractive index of fused quartz is 1.46 and that of sapphire is 1.77. If vq is the speed of light in quartz and vs is the speed of light in sapphire, then which one of the following relationships is correct?
- (a)vq > vs
- (b)vs > vq
- (c)vs = vq
- (d)vs = vq/2
Correct — A, vq > vs. The speed of light in a medium is v = c/n, so the higher the refractive index, the slower the light. Quartz has the lower refractive index (1.46) and sapphire the higher (1.77), so light travels faster in quartz: vq > vs.
- (b)vs > vq — This reverses the relationship; the higher-index sapphire slows light more, so its speed is lower, not higher.
- (c)vs = vq — The speeds would be equal only if the refractive indices were equal, which they are not (1.46 versus 1.77).
- (d)vs = vq/2 — There is no factor-of-two relation; the ratio of the speeds equals the inverse ratio of the refractive indices, vq/vs = 1.77/1.46, about 1.21.
Light slows down on entering a transparent medium, and the refractive index n measures how much: v = c/n, where c is the speed of light in vacuum. A medium with a higher refractive index is optically denser and slows light more. So comparing two media, the one with the smaller n allows the higher speed.
Just compare the two refractive indices — the smaller n (quartz, 1.46) gives the larger speed. The wrong choices come from reversing the relationship or inventing a numerical factor.
- The speed of light in a medium is v = c/n, where n is the refractive index.
- A higher refractive index (an optically denser medium) means slower light.
- Quartz (n = 1.46) is optically rarer than sapphire (n = 1.77), so light is faster in quartz: vq > vs.
- In vacuum n = 1 and the speed of light is maximum, about 3 x 10^8 m/s.
A lower refractive index means faster light, so vq > vs.
- Thinking a higher refractive index means a higher speed — it is the opposite.
- Confusing optical density with mass density.
Given the refractive indices of two media, compare the speeds of light — the higher-index medium is the slower one.
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.
- (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 refractive-index concept — diamond's HIGH refractive index (not low) makes it sparkle, just as the higher-index sapphire slows light more than quartz.
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
Answer(a) X < Y
The same v = c/n idea — light in carbon disulfide (a denser medium, n greater than 1) is slower than in vacuum, exactly as quartz beats sapphire here.
- practice — not a real PYQ
Light travels fastest in which of the following?
- (a)Glass
- (b)Water
- (c)Vacuum
- (d)Diamond
Answer(c) Vacuum — it has the lowest refractive index (n = 1).
- 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 x 10^8 m/s
- (b)2 x 10^8 m/s
- (c)4.5 x 10^8 m/s
- (d)1.5 x 10^8 m/s
Answer(b) 2 x 10^8 m/s — v = c/n = (3 x 10^8)/1.5.