Which one of the following materials cannot be used to make a convex lens?

Correct — A, Aluminium. A lens works by refraction, which means light has to enter the material, bend at the curved surfaces and emerge on the far side. That requires transparency, and aluminium is a metal. The sea of free electrons that makes a metal conduct electricity also makes it absorb and reflect visible light, so nothing gets through a piece of aluminium thick enough to be shaped into a lens. It makes a superb mirror instead, which is why aluminium is the standard reflective coating on telescope mirrors. Glass, sapphire and water are all transparent and all have a refractive index different from that of air, which is the only other thing a lens needs.

• (b)Glass — The ordinary material of lenses, with a refractive index of roughly 1.5. Every pair of spectacles and every camera answers this option.
• (c)Sapphire — A transparent crystalline form of aluminium oxide with a refractive index near 1.8, used for hard, scratch-resistant optical windows and lenses. The metal is opaque while its oxide crystal is clear, and that contrast is what makes this option worth pausing over.
• (d)Water — Transparent, with a refractive index of about 1.33. A drop of water on a leaf behaves as a converging lens, and water-filled lenses have been used to make adjustable spectacles.

A lens is a piece of transparent material with at least one curved surface. Light slows on entering it, bends towards or away from the normal at each surface, and emerges travelling in a new direction; a convex lens is shaped so that parallel rays converge to a focus. Two properties are needed of the material — it must transmit light, and its refractive index must differ from that of the surrounding medium, since a material matched exactly to its surroundings would bend nothing.

The elegance of this question is that it tests a property of metals through an optical question. Metals are opaque because their conduction electrons respond to the oscillating field of a light wave and re-radiate it, so visible light is reflected rather than transmitted. The same electrons make metals good conductors and good mirrors, and those two facts share one explanation. Sapphire is planted in the list to catch anyone who reasons that aluminium oxide contains aluminium and so must also be excluded; the crystal is an insulator with no free electrons and it is perfectly clear. Water is planted to catch anyone who thinks a lens must be solid. Neither of those matters, only transparency and a mismatch of refractive index.

• A lens works by refraction, so its material must transmit light and have a refractive index different from its surroundings.
• Approximate refractive indices are 1.33 for water, 1.5 for ordinary glass and about 1.8 for sapphire.
• Metals are opaque because their free electrons reflect and absorb visible light, which is the same property that makes them conduct.
• Aluminium is the standard reflective coating for telescope mirrors precisely because it reflects so well.
• Sapphire is crystalline aluminium oxide, also known as corundum, and it is transparent even though the metal it contains is not.

• Excluding sapphire because it contains aluminium; the oxide crystal is transparent while the metal is not.
• Assuming a lens has to be solid, which would wrongly rule out water.
• Confusing what makes a good mirror with what makes a good lens — for a metal they are opposite requirements.

Asked as a negative item where the single opaque material has to be picked out of three transparent ones, with a chemically related decoy included.

• practice — not a real PYQ

  Metals appear shiny and are opaque to visible light chiefly because of

  • (a)their high density
  • (b)their free electrons
  • (c)their crystalline structure
  • (d)their high melting point

  Answer(b) their free electrons — they re-radiate incident light, so it is reflected rather than transmitted.

• practice — not a real PYQ

  A convex lens made of glass is immersed in a liquid of the same refractive index as the glass. The lens will then

  • (a)converge light more strongly
  • (b)diverge light
  • (c)behave as a plane sheet and not bend light
  • (d)become opaque

  Answer(c) behave as a plane sheet and not bend light — refraction needs a difference in refractive index across the surface.