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.
Consider the following statements about the side-view mirror of the car:
(A) The laws of reflection hold at each point of the curved surface of the side-view mirror.
(B) The normal at the point of incidence on the side-view mirror is along the line joining that point to the pole.
(C) The magnification of the image of the car in the side-view mirror is negative.
(D) In the mirror equation, the distance of the car from the side-view mirror is taken as negative.
Which of the above statements are correct?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A) and (D) only
A curved mirror reflects light by the same laws as a plane mirror, point by point. Signs of distances and heights follow the Cartesian sign convention, with the pole as the origin.
(A) The laws of reflection hold at each point of the curved surface of the side-view mirror. — True. The laws of reflection apply at every point of any reflecting surface, plane or curved.
(B) The normal at the point of incidence on the side-view mirror is along the line joining that point to the pole. — False. The normal at a point of a spherical mirror is along the radius. So it lies along the line joining the point to the centre of curvature.
(C) The magnification of the image of the car in the side-view mirror is negative. — False. The image of the car is erect, so its height is measured upwards and is positive. The magnification is therefore positive.
(D) In the mirror equation, the distance of the car from the side-view mirror is taken as negative. — True. Light goes from the car towards the mirror. The car lies opposite to this direction from the pole, so \( u \) is negative.
NCERT (2026-27):
Reflection of Light by Spherical Mirrors – “… These laws are valid at each point on any reflecting surface whether plane or curved. …”
Reflection of Light by Spherical Mirrors – “… That is, the normal is along the radius, the line joining the centre of curvature of the mirror to the point of incidence.”
Summary – “… The heights measured upwards above x-axis and normal to the principal axis of the mirror/lens are taken as positive. …”
Sign convention – “… The distances measured in the same direction as the incident light are taken as positive and those measured in the direction opposite to the direction of incident light are taken as negative …”