The refractive indices of two media are denoted by n₁ and n₂, and the velocities of light in these two media are respectively v₁ and v₂. If n₂/n₁ is 1·5, which one of the following statements is correct?
- (a)v₁ is 1·5 times v₂.
- (b)v₂ is 1·5 times v₁.
- (c)v₁ is equal to v₂.
- (d)v₁ is 3 times v₂.
Correct — A, v₁ is 1·5 times v₂. The refractive index of a medium is defined as n = c/v, the speed of light in vacuum divided by its speed in that medium. Applying it to both media gives n₁ = c/v₁ and n₂ = c/v₂, so n₁v₁ = n₂v₂ = c. Rearranged, v₁/v₂ = n₂/n₁ = 1·5, which is exactly the statement in option (a). The physical sense is that refractive index and speed move in opposite directions: medium 2 has the larger index, so light travels more slowly in it, and medium 1 is the faster of the two by the same factor of one and a half.
- (b)v₂ is 1·5 times v₁. — This inverts the relationship. It would make light faster in the medium with the higher refractive index, which is the opposite of what a refractive index measures — a denser medium slows light down.
- (c)v₁ is equal to v₂. — Equal speeds would require equal refractive indices, that is n₂/n₁ = 1. The ratio is given as 1·5, so the two media cannot slow light equally.
- (d)v₁ is 3 times v₂. — The ratio of speeds is the inverse ratio of the indices, 1·5, not double that. A factor of 3 would need n₂/n₁ = 3, which is roughly the index of diamond compared with air, not the value given.
Light travels fastest in vacuum, at about 3 × 10⁸ metres per second, and more slowly in every material medium. The refractive index of a medium is the ratio of those two speeds, so it is a pure number greater than one that says by what factor the medium holds light back. Because the frequency of light is fixed by its source and does not change on entering a new medium, the drop in speed shows up as a shortening of the wavelength, and the bending of the ray at the boundary follows from that.
The whole question turns on remembering which way round n = c/v runs. Any candidate who writes the definition down first cannot go wrong; those who work from a vague sense that 'higher index means more' pick option (b). A quick sanity check is to think of a real pair of media — light travels about 2 × 10⁸ m/s in water, whose index is 1·33, and about 3 × 10⁸ m/s in air, whose index is very close to 1. The medium with the bigger number is the slower one. Notice too that the answer depends only on the ratio of the two indices, so no individual value is needed.
- Refractive index is defined as n = c/v, so n₁v₁ = n₂v₂ = c and the speeds are in the inverse ratio of the indices.
- Refractive index is dimensionless and, for ordinary transparent media, greater than one.
- The frequency of light does not change when it enters a new medium; the speed and the wavelength both change.
- Typical values are about 1·0003 for air, 1·33 for water, roughly 1·5 for ordinary glass and 2·42 for diamond.
The medium with the larger refractive index is the slower one, by exactly the same factor.
- Reading a high refractive index as 'light moves faster', when it means the opposite.
- Squaring or doubling the ratio; the speeds and the indices are in a simple inverse proportion.
- Assuming a change of medium alters the frequency of the light; it is the speed and wavelength that change.
Asked as a proportional-reasoning item where a single ratio is supplied and the definition of refractive index does the rest.
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
Rests on the same habit of reading a refractive index correctly. Diamond's index of about 2·42 is far above glass's 1·5, which is why the reason is false — and why light crawls more slowly through diamond than through glass.
If the absolute refractive indices of glass and water are 3/2 and 4/3 respectively, what will be the ratio of velocity of light in glass and water ?
- (a) 3 : 4
- (b) 4 : 3
- (c) 8 : 7
- (d) 8 : 9
Answer(d) 8 : 9
The same relation with real numbers rather than symbols. Inverting the index ratio (4/3) ÷ (3/2) gives 8 : 9, which is the calculation this question asks for in the abstract.
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
Answer(a) vq > vs
Asks only for the direction of the inequality, which is the single idea this item tests. The medium with the smaller index carries light faster.
- practice — not a real PYQ
The refractive index of water is 4/3 and that of glass is 3/2. In which medium does light travel faster, and by what factor?
- (a)Glass, by a factor of 9/8
- (b)Water, by a factor of 9/8
- (c)Glass, by a factor of 8/9
- (d)They are equal
Answer(b) Water, by a factor of 9/8 — the speeds are in the inverse ratio of the indices, so v_water/v_glass = (3/2)/(4/3) = 9/8.
- practice — not a real PYQ
When light passes from air into glass, which of the following remains unchanged?
- (a)Speed
- (b)Wavelength
- (c)Frequency
- (d)Direction
Answer(c) Frequency — it is set by the source; the speed and wavelength both fall in the denser medium, and the ray bends unless it strikes the surface normally.