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.
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): The image of Riya’s face in the make-up mirror is a virtual image.
Reason (R): An image is virtual when the reflected rays actually meet at the image point.
In the light of the above statements, choose the most appropriate answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A) is correct but (R) is not correct.
Assertion (A) The image of Riya’s face in the make-up mirror is a virtual image. — True. For the make-up mirror \( f=-30\ \mathrm{cm} \) and \( u=-10\ \mathrm{cm} \). The face is inside the focal length.
\( \begin{aligned} \frac{1}{v} &= \frac{1}{f}-\frac{1}{u} \\ &= -\frac{1}{30}+\frac{1}{10} \\ &= \frac{2}{30} \end{aligned} \)
\( v=+15\ \mathrm{cm} \)
A positive \( v \) puts the image 15 cm behind the mirror. No light reaches that point, so the image is virtual.
Reason (R) An image is virtual when the reflected rays actually meet at the image point. — False. When the reflected rays actually meet, the image is real. A virtual image is formed when the rays do not meet but only appear to come from the point.
NCERT (2026-27):
The mirror equation – “… The image is real if the rays actually converge to the point; it is virtual if the rays do not actually meet but appear to diverge from the point when produced backwards. …”
The mirror equation – “Dividing it by v, we get”
\( \displaystyle \frac{1}{v}+\frac{1}{u}=\frac{1}{f} \)\( \qquad (9.7) \)