BPSC 71st CCE Prelims General Studies · Question 127 of 150

Correct — D, Infinity. The focus of a mirror is defined entirely by what the mirror does to a beam of light travelling parallel to its principal axis: after reflection those rays either actually meet at a point (a concave mirror's real focus) or appear to spread out from a point behind the surface (a convex mirror's virtual focus). A flat reflecting surface has the same normal direction at every point on it, so by the law of reflection every ray in a parallel beam turns through the same angle and the beam emerges still parallel. Parallel lines never meet, and they do not appear to meet either, so a plane mirror has no focal point at any finite distance in front of or behind it. Saying 'the focal length is infinite' is simply the compact way of stating that. Two formal routes give the same answer, and either can be written in twenty seconds. First, a flat surface is the limiting case of a spherical surface whose radius of curvature has grown without bound: R = ∞. For spherical mirrors of small aperture NCERT gives R = 2f, so f = R/2 = ∞. Second, use the mirror formula 1/v + 1/u = 1/f. A plane mirror always places the image exactly as far behind the surface as the object stands in front of it, so in the New Cartesian convention v = −u. Substituting, 1/f = 1/(−u) + 1/u = 0, and a quantity whose reciprocal is zero is infinite. The same substitution also settles the magnification: m = −v/u = −(−u)/u = +1, so the image is erect and exactly life-size, which is the everyday experience of a bathroom mirror. Physically, an infinite focal length means zero converging or diverging power — a plane mirror changes the direction of a beam without changing its convergence at all. That is precisely why plane mirrors, and not curved ones, are used in a periscope — two of them set at 45° — and in a kaleidoscope, devices in which the beam has to be redirected or repeated without being focused at all. (The paper's phrase 'focal distance' is the Hindi फोकस दूरी rendered literally; the standard English term is focal length.)

• (a)+1 cm — A finite, positive focal length. In the New Cartesian convention that NCERT uses, a positive focal length belongs to a convex — that is, diverging — mirror, whose principal focus lies behind the reflecting surface. So +1 cm does not describe a flat sheet at all; it describes a strongly curved convex mirror of radius of curvature 2 cm, roughly the bulge of a small ball bearing. Any finite value, of either sign, asserts that the mirror bends parallel light towards or away from an axis, which a flat surface never does.
• (b)– 1 cm — A finite, negative focal length, which in the same convention means a concave — converging — mirror whose real focus sits 1 cm in front of the pole, i.e. a mirror of radius of curvature 2 cm: a shaving mirror shrunk to the size of a thumbnail. The option is tempting for two bad reasons. It half-matches the memory that mirror distances 'usually carry a minus sign', and it sits symmetrically opposite option (a), so a candidate feels that one of the pair must be the intended answer.
• (c)2 cm — The option engineered for someone who reaches for arithmetic before reading. It looks as though it has been derived from R = 2f, and a candidate who remembers that relation may supply an imaginary radius and halve or double it. But the question states no radius, no curvature and no length of any kind — there is not a single number in the stem. A numerical answer in centimetres would have to be invented, and a value that does not follow from anything given cannot be the answer to a physics question.

Every mirror is classified by what it does to a parallel beam. A concave mirror curves inwards, its normals converge, and a beam parallel to the principal axis is reflected to a genuine meeting point in front of the mirror — a real focus, which is why a concave mirror can burn paper and why it is used in solar concentrators, torch and headlight reflectors, and dentists' mirrors. A convex mirror curves outwards, the reflected rays diverge, and they only appear to come from a point behind the surface — a virtual focus, which spreads the view and is why vehicle rear-view mirrors are convex. The distance from the pole of the mirror to that focus is the focal length f, and for spherical mirrors of small aperture it is half the radius of curvature, R = 2f, so the focus lies midway between the pole and the centre of curvature. A plane mirror is the case where the sphere has become infinitely large: its surface has no curvature, one single normal direction, and therefore no meeting point at all. NCERT fixes the signs with the New Cartesian Sign Convention — the pole is the origin, the object always sits on the left so light arrives from the left, and distances measured to the right of the pole are positive while those to the left are negative. It follows that a convex mirror's focal length is positive and a concave mirror's is negative, a point students routinely invert. Whatever the object distance, a plane mirror gives an image that is virtual, erect, the same size as the object, laterally inverted, and as far behind the mirror as the object is in front.

There is a shortcut here that costs no physics at all, and it is worth internalising because BPSC uses this option pattern constantly. Read the four choices first: three of them are lengths in centimetres, and the stem contains no length, no radius, no curvature and no distance of any kind. A question that supplies no measurement cannot have an answer in centimetres, so (a), (b) and (c) are gone before a single formula is written, leaving only the non-numeric option. Then confirm it properly, because guessing by elimination is how a candidate gets the next question wrong: the image in a plane mirror always satisfies v = −u, and putting that into 1/v + 1/u = 1/f forces 1/f = 0 and f = ∞. That substitution is the single discriminating step. Two misreadings account for most of the ways to go wrong here. The first is confusing the focal length with the image distance. The image in a plane mirror is very much at a finite distance — stand 2 m from a mirror and your image is 2 m behind it — so a candidate who has silently substituted 'where is the image' for 'where is the focus' will look for a finite number and take one. The second is the instinct that 'infinity' is a non-answer, a way of saying the quantity does not exist. It is not. An infinite focal length is a precise physical statement, equivalent to saying the optical power is zero: the element redirects light without converging or diverging it. The same idea returns for lenses, where power P = 1/f in dioptres and an element of infinite focal length has zero power.

• Mirror formula: 1/v + 1/u = 1/f. For a plane mirror the image is as far behind as the object is in front, so v = −u, giving 1/f = 0 and f = ∞; the magnification m = −v/u then works out to exactly +1.
• For spherical mirrors of small aperture the radius of curvature is twice the focal length, R = 2f, so the principal focus lies midway between the pole and the centre of curvature. A plane surface is the R → ∞ limit, hence f = R/2 = ∞.
• NCERT's New Cartesian Sign Convention puts the pole at the origin with the object always on the left, and counts distances to the right of the pole as positive. Consequently a convex mirror has a POSITIVE focal length — NCERT's own worked example writes f = R/2 = +1.50 m because a convex mirror's focus lies behind it — while a concave mirror's focal length is negative.
• The image in a plane mirror is always virtual, erect, equal in size to the object, laterally inverted, and located as far behind the mirror as the object stands in front of it, for every object distance.
• A plane mirror only needs to be half a person's height, hung at the correct level, to show a full-length image, and this is true however far back the person stands — a direct consequence of the equal-angle law of reflection.
• Mirror choice follows the focal length: plane mirrors where light must be redirected but never focused (the periscope's pair of mirrors at 45°, the kaleidoscope); concave mirrors where convergence is wanted (solar concentrators, torch and headlight reflectors with the source at the focus, shaving and dentists' mirrors); convex mirrors where a wide, diminished field of view is wanted (vehicle rear-view mirrors, corner mirrors in shops).

• Assuming every mirror must have some finite focal length, so 'infinity' must be a trick answer — an infinite focal length is a precise statement meaning the mirror has zero converging or diverging power
• Confusing the focal length with the image distance: a plane mirror's image is at a perfectly finite distance behind the glass, but its focus is not
• Inverting the sign convention — under NCERT's New Cartesian rules a convex mirror's focal length is positive and a concave mirror's is negative, which is the reverse of what most candidates guess

BPSC asks optics as bare recall dressed up to look computational: a one-line stem, no data at all, and three numeric options in centimetres among which the real answer is the only word. Q127 sits inside a run of eleven school-physics items, Q121 to Q131, where the Commission's own remarks are simply the arithmetic. UPSC's optics questions from the same chapter are phenomenon-driven and ask why rather than how much — why an air bubble in water behaves as a diverging element, why a diamond sparkles more than cut glass, how far a reflected ray turns when the mirror turns, how an optical fibre or an endoscope works. Learn the definitions for BPSC; learn what each definition explains in the physical world for UPSC.

• practice — not a real PYQ

  A concave mirror has a radius of curvature of 20 cm. Following the New Cartesian sign convention, its focal length is

  • (a)+ 20 cm
  • (b)– 10 cm
  • (c)+ 10 cm
  • (d)– 20 cm

  Answer(b) – 10 cm — for a spherical mirror R = 2f, so the magnitude is 20 ÷ 2 = 10 cm, and the sign is negative because a concave mirror's principal focus lies in front of the mirror, on the same side as the incident light, which the convention counts as the negative direction.

• practice — not a real PYQ

  The image formed by a plane mirror is always

  • (a)real, inverted and of the same size as the object
  • (b)virtual, erect and of the same size as the object
  • (c)virtual, erect and diminished
  • (d)real, erect and magnified

  Answer(b) virtual, erect and of the same size as the object — the reflected rays only appear to come from behind the mirror, so the image cannot be caught on a screen, and since the image is as far behind as the object is in front, the magnification is exactly +1. A diminished virtual erect image is the signature of a convex mirror, not a plane one.