CDS (II) 2020 General Knowledge · Question 90 of 120

Correct — B, c/v. The absolute refractive index of a medium is defined as the speed of light in vacuum, taken as c and treated as the speed in air for practical purposes, divided by the speed of light in that medium, so n = c/v. Since light always slows down on entering a denser medium, v is smaller than c and the ratio comes out greater than one, which is what every real refractive index is — about 1.33 for water, 1.5 for ordinary glass, 2.42 for diamond. The formula also runs backwards, which is how these items are usually set: with n = 3/2 and c = 3 × 10⁸ m/s, the speed in the medium is v = c/n = 2 × 10⁸ m/s.

• (a)v/c — This is the reciprocal, and it would always give a number less than one. It is the inverse of the refractive index, not the index itself.
• (c)c/(2.v) — There is no factor of two in the definition. The 2 has been imported from some other formula and has no physical meaning here.
• (d)(c − v)/c — This expression is a fractional reduction in speed, not a refractive index. For glass it would give about 0.33, whereas the index of glass is 1.5.

Refraction is the bending of light as it crosses from one transparent medium into another, and it happens because light travels at different speeds in different media. Snell's law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant for a given pair of media, and that constant is the relative refractive index. The absolute refractive index of a medium is its index with respect to vacuum, n = c/v. Because n depends slightly on wavelength, a prism splits white light into its colours, which is dispersion.

Two checks make this item immediate. The first is the magnitude: a refractive index is always greater than one for a material medium, so any expression that would return a number below one can be discarded at sight, and that removes two options. The second is the direction of the effect: light slows in a denser medium, so the denser the medium the larger the index, which means the speed in the medium has to sit in the denominator. Between them these two checks leave only c/v standing. Remember also that n = c/v pairs with the wavelength relation, since frequency is unchanged on refraction while wavelength shortens in the same proportion as the speed.

• Absolute refractive index n = c/v, where c is the speed of light in vacuum or air and v the speed in the medium.
• Typical values are about 1.33 for water, 1.5 for ordinary glass and 2.42 for diamond; n is always greater than one for a material medium.
• With n = 3/2 and c = 3 × 10⁸ m/s, the speed of light in the medium is 2 × 10⁸ m/s.
• Snell's law gives the ratio of the sine of the angle of incidence to the sine of the angle of refraction as the relative refractive index of the pair of media.
• On refraction the frequency of light stays the same while its speed and wavelength change in the same ratio.

• Inverting the ratio and writing v/c, which would always give a value below one.
• Assuming the frequency of light changes on entering a medium. It is the speed and the wavelength that change.
• Treating the refractive index as a fixed property independent of colour; it varies with wavelength, which is why dispersion happens.

As a definition item, or as a numerical converting between the refractive index and the speed of light in a medium.

• practice — not a real PYQ

  The refractive index of a medium is 1.5 and the speed of light in air is 3 × 10⁸ m/s. The speed of light in the medium is

  • (a)1.5 × 10⁸ m/s
  • (b)2 × 10⁸ m/s
  • (c)3 × 10⁸ m/s
  • (d)4.5 × 10⁸ m/s

  Answer(b) 2 × 10⁸ m/s — from n = c/v, v = c/n = 3 × 10⁸ divided by 1.5.

• practice — not a real PYQ

  When light passes from air into glass, which one of the following remains unchanged?

  • (a)Speed
  • (b)Wavelength
  • (c)Frequency
  • (d)Direction

  Answer(c) Frequency — the speed and wavelength both fall in the ratio of the refractive index, while the frequency is set by the source.