In the context of the formation of images by spherical mirror, which of the following statements are correct?
(A) Magnification \( m \) is +ve for real images and -ve for virtual images.
(B) \( f \) and \( R \) are -ve for a concave mirror and +ve for a convex mirror.
(C) Magnification \( m \) has no units.
(D) For a real object, \( u \) is +ve and \( v \) is +ve for real image and -ve for virtual image.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (B) and (C) only
Take the Cartesian sign convention: distances are measured from the pole, positive in the direction of the incident light and negative against it.
(A) Magnification \( m \) is +ve for real images and -ve for virtual images. — Incorrect. A real image is inverted, so \( m \) is negative; a virtual image is erect, so \( m \) is positive.
(B) \( f \) and \( R \) are -ve for a concave mirror and +ve for a convex mirror. — Correct. The centre of curvature and the focus of a concave mirror lie in front of it, on the side the light comes from, so they are negative.
(C) Magnification \( m \) has no units. — Correct. It is a ratio of two lengths, \( m = h_{i}/h_{o} = -v/u \).
(D) For a real object, \( u \) is +ve and \( v \) is +ve for real image and -ve for virtual image. — Incorrect. A real object lies in front of the mirror, so \( u \) is negative. A real image also forms in front of a mirror, so \( v \) is negative for a real image and positive for a virtual image, the opposite of what is stated.
NCERT (2026-27):
Summary – “… 3. Cartesian sign convention: Distances measured in the same direction as the incident light are positive; those measured in the opposite direction are negative. All distances are measured from the pole/optic centre of the mirror/lens on the principal axis.”
Summary – “… f is (approximately) half the radius of curvature R. f is negative for concave mirror; f is positive for a convex mirror.”