Consider the following statements: Statement I: Light travels faster in air than in water. Statement II: Refractive index of air is greater than that of water. Select the correct option:
- (a)Statement I is correct, Statement II is wrong
- (b)Statement I is wrong, Statement II is correct
- (c)Both statements are correct and Statement II is the correct explanation of Statement I
- (d)Both statements are correct but Statement II is not the correct explanation of Statement I
Correct — A, Statement I is correct, Statement II is wrong.
Light moves fastest in vacuum, and air slows it only slightly: its refractive index is about 1.0003. Water's is about 1.33. Statement I therefore stands — light does travel faster in air than in water.
Statement II reverses that comparison. Water carries the larger refractive index of the two, so the claim that air's is greater is false. The grading is Statement I is correct, Statement II is wrong.
The idea to carry away is that refractive index and speed run in opposite directions, because n = c/v. The medium with the bigger index is the one in which light is slower.
- (b)Statement I is wrong, Statement II is correct — Both halves fail here. Light is genuinely faster in air than in water, so Statement I is not wrong, and air's index of about 1.0003 is the smaller value, so Statement II is not correct.
This grading fits a pair whose speed claim is the false half and whose index claim is the true half — say, 'light travels faster in water than in air' set against 'water's refractive index exceeds that of air'.
- (c)Both statements are correct and Statement II is the correct explanation of Statement I — This option needs both statements to be true before the explanatory question is even reached, and Statement II is false: water sits near 1.33 while air sits near 1.0003.
Option c is the right answer to an assertion-reason pair whose reason is true and does account for the assertion — for instance, 'light slows on entering water' explained by 'water has the higher refractive index'.
- (d)Both statements are correct but Statement II is not the correct explanation of Statement I — Like option c, this one requires Statement II to be true, and as printed it is not. Once the second statement fails on its own facts, the explanatory half of the option stops mattering.
Option d belongs to a pair of separately true statements with no causal link — the reason is accurate on its own but does not account for the assertion.
Refractive index is defined by the ratio n = c/v — the speed of light in vacuum divided by its speed in the medium. Because v sits in the denominator, a larger n means light moves more slowly through that medium.
Vacuum takes n = 1 by definition. Air is barely different at about 1.0003, water is about 1.33, and ordinary crown glass about 1.5.
An assertion-reason item asks two things in sequence: whether each statement is true on its own, and, only if both survive, whether the second explains the first. The four options encode those two judgements.
This pair is settled at the first stage. The reason inverts the very index comparison that the assertion rests on, so the explanation question does not arise.
- Refractive index is n = c/v, the speed of light in vacuum divided by its speed in the medium.
- Air's refractive index for visible light is about 1.0003, only just above vacuum's value of 1.
- Water's refractive index is about 1.33, giving a light speed of about 2.26 × 10⁸ m/s.
- Because n = c/v, the medium with the higher refractive index is the one in which light travels slower.
- A ray passing from air into water bends towards the normal, the behaviour expected on entering a higher-index medium.
- The frequency of light is unchanged on crossing from air into water, while its speed and wavelength both fall.
Air holds the smaller index of the two highlighted rows, so light runs faster in air — Statement I holds, while Statement II turns the index comparison the wrong way round.
- Grading the two statements as a package. Statement I being true carries no information about Statement II, and the option set rewards judging each on its own facts.
- Inverting n = c/v. A larger refractive index means a smaller speed, so water's higher index makes light slower in water, not faster.
- Reading the air-versus-water index comparison the wrong way round; air's value of about 1.0003 is the smaller of the pair.
- Treating refractive index as a measure of how clear a medium looks. It measures how much the medium slows light, not how transparent it is.
- Overlooking that options c and d both need Statement II to be true, so settling the index comparison narrows the choice to a or b.
The n = c/v relation appears in several shapes: as direct formula recall, as arithmetic where an index and c are given and the speed is wanted, and as a comparison where two indices must be turned into an ordering of speeds.
The assertion-reason wrapper adds a further layer, pairing a speed claim with an index claim that may point the same way or the opposite way.
NDA_GAT_2020_I_II_Q1492020Same relation between refractive index and speed: quartz at 1.46 against sapphire at 1.77, where the higher index gives the lower speed. It differs in asking for an ordering of two solids from stated numbers, whereas the UKPSC item asks whether a stated index comparison between air and water is true at all.
CDS_GK_2020_II_Q902020States the underlying formula itself — the refractive index of a medium is c/v. That is the rule Statement II here depends on, but the CDS item stops at the definition, while this one applies it to two named media and grades a statement pair.
CDS_GK_2020_I_Q112020The same relation used numerically: with an index of 3/2 the speed drops to 2 × 10⁸ m/s. The arithmetic demonstrates that a higher index slows light, which is the qualitative point the UKPSC item turns on; the CDS version wants a calculation rather than a truth judgement.
- practice — not a real PYQ
The refractive index of a transparent medium is 1.25. If the speed of light in vacuum is 3 × 10⁸ m/s, the speed of light in that medium is
- (a)2.4 × 10⁸ m/s
- (b)3.75 × 10⁸ m/s
- (c)1.25 × 10⁸ m/s
- (d)3 × 10⁸ m/s
Answera — v = c/n = (3 × 10⁸)/1.25 = 2.4 × 10⁸ m/s.Option b multiplies instead of dividing, which would put light faster in the medium than in vacuum. Option c copies the index across as though it were a speed. Option d leaves the speed unchanged, which would need an index of 1.
- practice — not a real PYQ
Consider the following statements: Statement I: A ray of light bends towards the normal when it passes from air into water. Statement II: The refractive index of water is greater than that of air. Select the correct option:
- (a)Statement I is correct, Statement II is wrong
- (b)Statement I is wrong, Statement II is correct
- (c)Both statements are correct and Statement II is the correct explanation of Statement I
- (d)Both statements are correct but Statement II is not the correct explanation of Statement I
Answerc — both statements are true, and the second is the reason for the first.By Snell's law a ray entering a medium of higher refractive index bends towards the normal, so water's larger index is precisely why the bending occurs.
Options a and b each mark one of two true statements false. Option d denies an explanatory link that Snell's law supplies.
- practice — not a real PYQ
Light travels slowest in which one of the following media?
- (a)Air (refractive index about 1.0003)
- (b)Water (refractive index about 1.33)
- (c)Crown glass (refractive index about 1.5)
- (d)Diamond (refractive index about 2.42)
Answerd — since v = c/n, the largest refractive index gives the smallest speed, and diamond's 2.42 is the largest of the four values printed.Air at about 1.0003 gives the fastest passage, so option a is the reverse of what is asked. Water and crown glass fall between the two, making options b and c slower than air but faster than diamond.