CDS (I) 2020 General Knowledge · Question 11 of 120

Correct — A, 2 × 10⁸ m/s. The refractive index of a medium is the speed of light in air divided by the speed of light in that medium. Rearranged, the speed in the medium is the speed in air divided by the refractive index. Here that is 3 × 10⁸ divided by 3/2, which is 3 × 10⁸ multiplied by 2/3, giving 2 × 10⁸ metres per second. The sense of the result is a check in itself: a refractive index greater than one means light is slower in the medium than in air, so the answer must be smaller than 3 × 10⁸, and 2 × 10⁸ is. This is NCERT's own exercise, which asks for the speed of light in glass of refractive index 1.50 given a vacuum speed of 3 × 10⁸ metres per second, with 1.50 written here as a fraction.

• (b)9/4 × 10⁸ m/s — Comes from dividing by 4/3 instead of 3/2, or from mishandling the fraction. It is 2.25 × 10⁸, which no consistent route from these numbers produces.
• (c)3/2 × 10⁸ m/s — This is the refractive index itself carried across as if it were a speed. It amounts to dividing 3 × 10⁸ by 2, which is not the relation.
• (d)3 × 10⁸ m/s — The speed in air, unchanged. Light can only equal this in a medium of refractive index one, and a refractive index of 3/2 says the medium slows it down.

Light travels fastest in vacuum, at very nearly 3 × 10⁸ metres per second, and slower in every material medium. The absolute refractive index of a medium is the ratio of the speed in air to the speed in that medium, so it is always greater than one for ordinary transparent materials. A larger refractive index means a slower speed and a more strongly bent ray at the surface.

The only place a candidate loses this mark is in the arithmetic of dividing by a fraction, and the paper prints the index as 3/2 rather than 1.5 for exactly that reason. Dividing by 3/2 is multiplying by 2/3. If the fraction feels risky under time pressure, convert it — 3 × 10⁸ divided by 1.5 is 2 × 10⁸ — and then sanity-check the direction, because the answer has to be smaller than the speed in air. Useful reference values from NCERT's table: water 1.33, crown glass 1.52, diamond 2.42. A refractive index of 3/2, or 1.5, is a good stand-in for ordinary glass, and benzene sits at exactly 1.50.

• Absolute refractive index equals the speed of light in air divided by the speed of light in the medium.
• The speed of light in vacuum is about 3 × 10⁸ metres per second.
• Light slows in a denser medium, so a refractive index above one always means a reduced speed.
• NCERT's table gives water 1.33, kerosene 1.44, benzene 1.50, crown glass 1.52 and diamond 2.42.
• The frequency of light does not change on entering a new medium; the speed and the wavelength both do.

• Multiplying by the refractive index instead of dividing, which makes light speed up in glass.
• Fumbling the division by a fraction; dividing by 3/2 is multiplying by 2/3.
• Assuming the frequency changes along with the speed; it does not.

As a one-step numerical of this kind, or in words — given two media and their refractive indices, in which does light travel faster.

• practice — not a real PYQ

  The refractive index of diamond is 2.42. Taking the speed of light in air as 3 × 10⁸ m/s, the speed of light in diamond is closest to

  • (a)1.24 × 10⁸ m/s
  • (b)2.42 × 10⁸ m/s
  • (c)3.00 × 10⁸ m/s
  • (d)7.26 × 10⁸ m/s

  Answer(a) 1.24 × 10⁸ m/s — divide 3 × 10⁸ by 2.42.

• practice — not a real PYQ

  Light travels through kerosene, water and diamond, whose refractive indices are 1.44, 1.33 and 2.42. In which of these is its speed greatest?

  • (a)Kerosene
  • (b)Water
  • (c)Diamond
  • (d)The speed is the same in all three

  Answer(b) Water — the lowest refractive index of the three, so the least slowing.