NDA (I) 2018 General Ability Test · Question 61 of 150

Correct — A, Reflection of light. A simple periscope is a tube with two plane mirrors fixed at its two ends, each tilted at forty-five degrees to the tube and facing each other. Light from an object above strikes the upper mirror, is turned through ninety degrees down the tube, strikes the lower mirror and is turned through ninety degrees again into the observer's eye. Both turns are ordinary reflection at a plane mirror, obeying the law that the angle of incidence equals the angle of reflection. Nothing in the simple instrument bends light by passing it through a medium, so reflection is the whole of its working principle.

• (b)Refraction of light — Refraction is the bending of light as it passes from one medium into another, and it is what lenses do. A simple periscope has no lens in the optical path; the light travels through air and is only turned by mirrors.
• (c)Dispersion of light — Dispersion is the splitting of white light into its colours, as a prism does and as a rainbow shows. A periscope must deliver the scene unchanged in colour, so dispersion would be a defect in it rather than its principle.
• (d)Total internal reflection of light — This is the closest distractor and worth taking seriously. Better periscopes do replace the mirrors with right-angled glass prisms, and those work by total internal reflection, which gives brighter images without a silvered surface to tarnish. But the question says a simple periscope, and the simple form uses plain mirrors — so ordinary reflection is the answer.

Reflection at a plane mirror obeys two laws — the incident ray, the reflected ray and the normal at the point of incidence all lie in one plane, and the angle of incidence equals the angle of reflection. A mirror tilted at forty-five degrees therefore turns a ray through a right angle. A periscope stacks two such turns so that the line of sight is displaced sideways or upwards while remaining parallel to itself, which lets an observer see over a wall, around a corner or above the surface of the sea.

The item turns on the single word 'simple', which is the examiner's way of pointing you at the mirror version rather than the prism version. That distinction is worth learning properly rather than dismissing, because it recurs. Simple periscope and simple kaleidoscope work by reflection at plane mirrors; prism binoculars and optical fibres work by total internal reflection; the lens of a camera or the eye works by refraction; a prism splitting sunlight shows dispersion. Total internal reflection additionally requires light to be travelling from a denser medium to a rarer one and to strike the boundary beyond the critical angle, and none of those conditions arise inside a tube full of air with two mirrors in it.

• A simple periscope uses two plane mirrors inclined at 45 degrees at the two ends of a tube.
• The laws of reflection state that the angle of incidence equals the angle of reflection and that both rays and the normal lie in one plane.
• Prism periscopes and prism binoculars use total internal reflection instead of silvered mirrors.
• Total internal reflection needs light going from a denser to a rarer medium at an angle beyond the critical angle.
• The image formed by a plane mirror is virtual, erect, of the same size as the object and laterally inverted.

• Missing the word 'simple' and answering for the prism periscope instead.
• Confusing total internal reflection with ordinary reflection at a mirror.
• Assuming any optical instrument must involve lenses and therefore refraction.

NDA asks which phenomenon underlies a named instrument or everyday sight — the periscope, the mirage, the twinkling of stars, the reddening of the setting Sun.

• practice — not a real PYQ

  The shining appearance of a diamond is chiefly due to

  • (a)reflection at a plane surface
  • (b)total internal reflection
  • (c)dispersion only
  • (d)diffraction

  Answer(b) total internal reflection — a diamond's very small critical angle traps light inside until it emerges through the crown.

• practice — not a real PYQ

  In a simple periscope the two plane mirrors are inclined to the axis of the tube at

  • (a)30 degrees
  • (b)45 degrees
  • (c)60 degrees
  • (d)90 degrees

  Answer(b) 45 degrees — that setting turns each ray through a right angle, so two mirrors shift the line of sight while keeping it parallel.