Read the following passage and answer the questions.
Riya uses a concave make-up mirror of radius of curvature 60 cm. She holds her face 10 cm in front of it. In the morning the mirror stands on a sunny window sill. A narrow parallel beam of sunlight then falls on it at a small angle to its principal axis. Her father’s car has a convex side-view mirror of radius of curvature 2 m. Sitting in the parked car, he watches another car come up from behind at a steady speed. He looks at it in the mirror when it is 19 m away and again when it is 4 m away. Both mirrors are small compared with their radii of curvature, so all the rays are paraxial. All distances are measured from the pole of each mirror, using the Cartesian sign convention.
After reflection from the make-up mirror, the beam of sunlight meets at a point that lies
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → in the plane through the focus, normal to the principal axis
Paraxial rays parallel to the principal axis meet at the principal focus F after reflection from a concave mirror. A parallel beam that makes a small angle with the axis also meets at one point. That point is at the same distance from the pole, but it lies off the axis.
Option (1) at the principal focus, on the principal axis — Incorrect. Only a beam parallel to the principal axis meets at F itself. The sunlight in this case is tilted to the axis, so it meets at a point away from the axis.
Option (2) at the centre of curvature of the mirror — Incorrect. A ray through the centre of curvature comes back along its own path. A parallel beam meets at a distance \( f=R/2 \) from the pole, which is only half way to C.
Option (3) on the principal axis, midway between the focus and the pole — Incorrect. For this mirror \( R=60\ \mathrm{cm} \), so \( f=30\ \mathrm{cm} \). The parallel beam meets 30 cm from the pole, and a point midway between F and P is only 15 cm from it.
Option (4) in the plane through the focus, normal to the principal axis — Correct. The tilted parallel beam meets at a point in the focal plane, the plane through F normal to the axis. This plane is 30 cm in front of the mirror.
NCERT (2026-27):
Focal length of spherical mirrors – “… If the parallel paraxial beam of light were incident, making some angle with the principal axis, the reflected rays would converge (or appear to diverge) from a point in a plane through F normal to the principal axis. This is called the focal plane of the mirror …”