CDS (I) 2021 General Knowledge · Question 106 of 120

Correct — B, Parabolic mirror. A spoon is a shiny curved reflecting surface — its inner face works as a concave mirror and its outer face as a convex one, which is why your reflection in the bowl of a spoon is upside down on one side and upright on the other. The stem removes the usual approximation by saying the spoon is non-spherical, and among the four options that leaves only one curved-mirror choice. The shape is also physically apt: a spoon bowl is deeper and narrower than a sphere would be, closer to a paraboloid, and a paraboloid is the surface that brings a parallel beam to a single sharp focus without the blurring that a spherical mirror suffers at its edges. The same geometry is used deliberately in torch and headlight reflectors, satellite dishes and reflecting telescopes.

• (a)Spherical mirror — The everyday classroom answer, and the one the stem has been written to exclude. School texts do treat a spoon as a spherical mirror as an approximation, but this paper says 'non-spherical' in the first line.
• (c)Plane mirror — A plane mirror is flat and always gives an image the same size as the object, the right way up and behind the glass. A spoon does none of that; the reflection changes size and flips as you turn the spoon over.
• (d)Lens — A lens works by refraction, bending light that passes through it. A spoon is opaque and metallic and works by reflection, so it cannot be a lens whatever its curvature.

Curved reflecting surfaces are classified by the shape they are cut from. A spherical mirror is part of a sphere and is easy to make, but rays striking it far from the axis meet at slightly different points, blurring the focus — the defect called spherical aberration. A parabolic mirror is cut from a paraboloid and gathers a whole parallel beam to one point exactly, which is why it is used wherever the focus has to be sharp or the outgoing beam has to be truly parallel.

Almost everything about this item is decided by one word in the stem. Take 'non-spherical' out and the intended school answer would be (a), because that is how the spoon is introduced in the chapter on light. With it in, the candidate has to notice that the paper is asking for a curved mirror that is not a sphere, and the option list supplies exactly one. Working by elimination reaches the same place: a plane mirror is not curved, and a lens is not a mirror. The useful takeaway is why anyone bothers with the parabola — a torch reflector has to send out a parallel beam, and only the parabolic shape does that cleanly from a source at its focus.

• The inner surface of a spoon acts as a concave mirror and the outer surface as a convex one.
• A parabolic mirror brings a parallel beam to a single sharp focus, avoiding the spherical aberration of a spherical mirror.
• Reversing the path, a source placed at the focus of a parabolic mirror sends out a parallel beam — the principle of a torch and a headlight reflector.
• Satellite dishes and reflecting telescopes use parabolic reflectors for the same reason.
• A lens forms images by refraction; a mirror forms them by reflection.

• Answering 'spherical mirror' from memory of the textbook example and missing the word 'non-spherical' in the stem.
• Confusing a curved mirror with a lens because both can magnify.
• Assuming the outer surface of a spoon behaves the same way as the inner one — one is concave, the other convex.

As an everyday-object item on curved mirrors, or as an application question about torch reflectors, dishes and telescopes.

• practice — not a real PYQ

  The reflector behind the bulb of a torch is shaped so that the light leaves as a parallel beam. For that, the bulb must be placed

  • (a)beyond the centre of curvature
  • (b)at the focus of the reflector
  • (c)between the pole and the focus
  • (d)at the pole

  Answer(b) at the focus of the reflector — rays leaving a source at the focus of a concave or parabolic reflector come back parallel to the axis.

• practice — not a real PYQ

  When you look at your face in the outer surface of a steel spoon, the image seen is

  • (a)inverted and magnified
  • (b)erect and diminished
  • (c)inverted and of the same size
  • (d)erect and magnified

  Answer(b) erect and diminished — the outer surface is convex, and a convex mirror always gives a small, upright, virtual image.