CDS (II) 2023 General Knowledge · Question 38 of 120

Correct — A, A light beam travelling from a rare medium to a dense medium slows down and bends towards the normal. The two halves of the statement are linked, and the first half causes the second. What makes one medium optically denser than another is that light moves more slowly in it: the refractive index of a medium is the speed of light in vacuum divided by its speed in that medium, so a higher index means a lower speed. Air has an index of about 1.0003, water about 1.33 and ordinary glass about 1.5, so a beam passing from air into glass slows to roughly two-thirds of its former speed. The bending follows from the slowing. A wavefront striking the surface obliquely reaches the new medium at one edge first, and that edge slows while the rest of the front is still travelling fast, so the front pivots — exactly as a marching column swings round when the ranks on one side shorten their stride. The pivot turns the ray towards the normal. Snell's law states the same thing quantitatively: n₁ sin i = n₂ sin r, so when n₂ is greater than n₁ the angle of refraction r must be smaller than the angle of incidence i, which is what 'towards the normal' means.

• (b)A light beam travelling from a rare medium to a dense medium speeds up and bends towards the normal. — Gets the bending right and the speed backwards. Light cannot speed up on entering a denser medium — being slower in that medium is precisely what makes it optically denser, and it is the slowing that produces the bending in the first place.
• (c)A light beam travelling from a rare medium to a dense medium slows down and bends away from the normal. — Gets the speed right and the bending backwards. Bending away from the normal is what happens on the return journey, from a dense medium into a rarer one, and it is that case which can lead to total internal reflection beyond the critical angle.
• (d)A light beam travelling from a rare medium to a dense medium speeds up and bends away from the normal. — Both halves are wrong. This describes light emerging from glass into air, not entering glass from air.

Refraction is the change in direction that a wave undergoes when it crosses into a medium in which its speed is different. The refractive index n of a medium is c divided by v, the speed of light in vacuum divided by its speed in the medium, and it is always at least one. Snell's law, n₁ sin i = n₂ sin r, ties the two angles to the two indices. The frequency of the light does not change on refraction — it is set by the source — so the wavelength changes in step with the speed. A ray striking the surface along the normal, at an angle of incidence of zero, slows down but is not deflected, because there is no oblique wavefront to pivot.

The way to keep the two cases apart is to remember the direction of travel rather than a rule about denser and rarer. Going in — air to glass, air to water — the light slows and hugs the normal. Coming out — glass to air, water to air — it speeds up and swings away from the normal, and if the angle inside is large enough it stops emerging altogether and is totally internally reflected, which is how an optical fibre and a diamond's sparkle both work. Note also that 'optically denser' is not the same as 'physically denser': it refers only to the refractive index, and there are materials with a lower mass density but a higher index than others. Everyday consequences follow directly — a stick looks bent where it enters water, a coin in a bowl appears raised, and stars twinkle because the atmosphere's varying layers keep refracting their light by slightly different amounts.

• Refractive index is the speed of light in vacuum divided by its speed in the medium, so a larger index means a slower speed in that medium.
• Approximate indices: air 1.0003, water 1.33, ordinary glass about 1.5, diamond about 2.42.
• Snell's law is n₁ sin i = n₂ sin r; entering a denser medium makes the angle of refraction smaller than the angle of incidence.
• Light entering a denser medium at right angles to the surface — an angle of incidence of zero — slows but does not bend.
• On the reverse path, dense to rare, light bends away from the normal, and beyond the critical angle it is totally internally reflected.

• Reversing the pair of facts: light slows in a denser medium, it does not speed up, and it is the slowing that turns it towards the normal.
• Applying the rare-to-dense rule to a ray leaving glass or water; the bending goes the other way on the way out.
• Assuming a ray always bends. At normal incidence the speed changes but the direction does not.

As a single statement to be judged correct or incorrect, as a ray-path identification, or as a numerical using Snell's law or the critical angle.

• practice — not a real PYQ

  A ray of light passes from water into air at an angle of incidence of 30 degrees. Compared with the incident ray, the refracted ray will

  • (a)bend towards the normal and slow down
  • (b)bend away from the normal and speed up
  • (c)bend towards the normal and speed up
  • (d)travel undeviated at the same speed

  Answer(b) bend away from the normal and speed up — water is the denser medium, so on leaving it the light gains speed and turns away from the normal.

• practice — not a real PYQ

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

  • (a)Its speed
  • (b)Its wavelength
  • (c)Its frequency
  • (d)Its direction of travel

  Answer(c) Its frequency — the frequency is fixed by the source, so it survives the crossing; speed and wavelength both fall, and an oblique ray also changes direction.