The focal distance of a plane mirror is

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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.)

Why the other options are wrong — (a) 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) 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) 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.

Concept: 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.

State PCS 2025 Q127 — Science & Technology PYQ with Answer

State PCS 2025 Q127 — Science & Technology PYQ with Answer