NDA (I) 2018 General Ability Test · Question 103 of 150

Correct — D, It is always greater than one. The refractive index of a medium with respect to air is the ratio of the speed of light in air to its speed in that medium. Light travels faster in air than in any ordinary transparent solid or liquid, so the ratio has a bigger number on top and comes out above one — about 1·33 for water, roughly 1·5 for common glass, 1·46 for fused quartz, 1·77 for sapphire and 2·42 for diamond. Because it is a ratio of two speeds it has no units, and because both speeds are positive and finite it can be neither negative nor zero. Being greater than one is also why a ray bends towards the normal on entering the medium.

• (a)It can be either positive or negative — A speed cannot be negative, so the ratio of two speeds cannot be either. What does carry a sign in optics is the focal length of a lens or mirror under the sign convention, and it is that convention students are half-remembering when they pick this option.
• (b)It can have zero value — A refractive index of zero would mean light travelled at infinite speed inside the material, which nothing does. Even the fastest medium for light is a vacuum, and light's speed there is finite.
• (c)It is unity for all materials — If every material had an index of one, no ray would ever bend at a boundary — no lens would focus, no prism would split white light, and a straw would look straight in a glass of water. The index is close to one only for air itself, at about 1·0003.

Refractive index measures how much a medium slows light down. Absolute refractive index compares the speed in vacuum with the speed in the medium; relative refractive index compares the speeds in two named media. Since air is barely denser optically than vacuum, an index quoted 'with respect to air' is for practical purposes the absolute index. The index also governs refraction through Snell's law, n₁ sin i = n₂ sin r, and sets the critical angle beyond which total internal reflection takes over.

The stem is carefully worded and a candidate should notice why. It says a material medium with respect to air, which is what keeps the answer above one — the relative index of air with respect to water is the reciprocal, about 0·75, and is therefore less than one. A UPSC prelims item has been built on exactly that reversal, asking what an air bubble in water behaves like; the answer is a diverging lens, because the bubble is the optically rarer medium. Two honest footnotes for a curious student. First, the index depends on the colour of the light — it is larger for violet than for red, which is why a prism separates the spectrum at all — so a textbook figure such as 1·5 for glass is a value for average visible light. Second, the statement 'always greater than one' is a claim about ordinary transparent materials and visible light; at X-ray frequencies, and in engineered metamaterials, physicists do meet indices below one, and that research is what the phrase 'negative refractive index' in the news refers to. None of that touches the school-level claim being tested here.

• Refractive index is a ratio of two speeds, so it is a pure number with no unit.
• Approximate values: water 1·33, fused quartz 1·46, ordinary glass about 1·5, sapphire 1·77, diamond 2·42.
• The index of air is about 1·0003, so an index measured against air is very nearly the absolute index.
• A higher index means a slower speed inside the medium and a sharper bend towards the normal on entry.

• Confusing the sign convention for focal length with a sign on the refractive index.
• Forgetting that reversing the two media inverts the ratio and can push it below one.
• Quoting a single index for a material without noticing that it changes with the colour of the light.

NDA usually sets this either as a property statement like this one or as a speed comparison — given two indices, decide in which medium light moves faster.

• practice — not a real PYQ

  The refractive index of a medium with respect to air is 1·5. The speed of light in that medium, taking the speed in air as c, is about

  • (a)1·5 c
  • (b)c
  • (c)2c/3
  • (d)3c/2

  Answer(c) 2c/3 — since n = c/v, v = c/1·5, which is two-thirds of c.

• practice — not a real PYQ

  Refractive index has which of the following units?

  • (a)metre per second
  • (b)dioptre
  • (c)no unit
  • (d)radian

  Answer(c) no unit — it is the ratio of two speeds, so the units cancel.