Match List-I with List-II. Use the Cartesian sign convention.
| List-I | List-II |
|---|---|
| (A) Magnification produced by a thin lens | (I) \( \frac{v}{u} \) |
| (B) Magnification produced by a spherical mirror | (II) \( -\frac{v}{u} \) |
| (C) Sign of the image distance \(v\) for a real image formed by a concave mirror | (III) Negative |
| (D) Sign of the image distance \(v\) for a real image formed by a convex lens | (IV) Positive |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A)-(I), (B)-(II), (C)-(III), (D)-(IV)
(A) Magnification produced by a thin lens — This matches (I) \( \frac{v}{u} \). For a real image of a lens, \(u\) and \(v\) have opposite signs. So \(m\) comes out negative for the inverted image without any extra sign.
(B) Magnification produced by a spherical mirror — This matches (II) \( -\frac{v}{u} \). For a real image of a mirror, \(u\) and \(v\) have the same sign. The minus sign is needed to make \(m\) negative.
(C) Sign of the image distance \(v\) for a real image formed by a concave mirror — This matches (III). The real image forms in front of the mirror, on the side of the object. To reach it from the pole we go against the incident light, so \(v\) is negative.
(D) Sign of the image distance \(v\) for a real image formed by a convex lens — This matches (IV). The real image forms on the far side of the lens. That distance is measured along the incident light, so \(v\) is positive.
NCERT (2026-27):
Refraction by a lens – “… it is easily seen that for a lens”
\( \displaystyle \frac{h^{\prime}}{h}=\frac{v}{u} \qquad (9.24) \)
The mirror equation – “… so that”
\( \displaystyle m=\frac{h^{\prime}}{h}=-\frac{v}{u} \qquad (9.9) \)
The mirror equation – “… To reach the object AB, image A′B′ as well as the focus F from the pole P, we have to travel opposite to the direction of incident light. Hence, all the three will have negative signs. Thus, B′ P = –v, FP = –f, BP = –u”
Refraction by a lens – “… Applying the sign convention, BO = – u, DI = +v, we get”