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.
As the car behind comes closer at a steady speed, its image in the side-view mirror
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → moves faster and faster as the car comes closer
For the side-view mirror \( f=+1\ \mathrm{m} \). The image of a far car lies just behind the mirror, close to the focus. The mirror equation shows how much the image shifts when the car moves by 1 m at two places.
The car moves from 19 m to 18 m. The image moves from 19/20 m to 18/19 m, a shift of only about 0.003 m.
The car moves from 4 m to 3 m. The image moves from 0.80 m to 0.75 m, a shift of 0.05 m.
The car takes the same time for each metre, so the image covers a larger distance in that time as the car comes nearer.
Option (1) moves faster and faster as the car comes closer — Correct. Each metre moved by the car shifts the image more when the car is near. So the speed of the image keeps rising as the car comes closer.
Option (2) moves at the same steady speed as the car — Incorrect. While the car covers many metres, the image stays within 1 m behind the mirror, between the pole and the focus. So the image moves much more slowly than the car.
Option (3) moves at a steady speed much smaller than that of the car — Incorrect. The image does move slowly, but its speed is not steady. The shift for each metre changes from about 0.003 m to 0.05 m.
Option (4) moves slower and slower as the car comes closer — Incorrect. This is the reverse of what happens. The image moves slowly when the car is far and faster when the car is near.
NCERT (2026-27):
Example 9.4 – “Although the jogger has been moving with a constant speed, the speed of his/her image appears to increase substantially as he/she moves closer to the mirror. …”