Consider the following statements about reflection by spherical mirrors:
(A) The relation \( f=R/2 \) holds for paraxial rays, that is, rays close to the pole that make small angles with the principal axis.
(B) For a convex mirror, the reflected rays of a parallel paraxial beam converge at a point F on its principal axis.
(C) A ray directed towards the centre of curvature of a convex mirror goes back along its own path after reflection.
(D) The mirror equation is valid for a concave mirror but not for a convex mirror.
(E) In the Cartesian sign convention, distances measured opposite to the direction of the incident light are negative.
Which of the above statements are correct?
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A), (C) and (E) only
The statements deal with the focal length, the ray rules and the sign rules for spherical mirrors.
(A) The relation \( f=R/2 \) holds for paraxial rays, that is, rays close to the pole that make small angles with the principal axis. — True. The result \( f=R/2 \) uses \( \tan\theta\approx\theta \). This is right only for small angles, that is, for paraxial rays.
(B) For a convex mirror, the reflected rays of a parallel paraxial beam converge at a point F on its principal axis. — False. A convex mirror spreads the reflected rays apart. They do not meet. They only appear to diverge from the focus F behind the mirror.
(C) A ray directed towards the centre of curvature of a convex mirror goes back along its own path after reflection. — True. Such a ray falls along the normal to the mirror. So it is sent back along the same line.
(D) The mirror equation is valid for a concave mirror but not for a convex mirror. — False. With the proper signs, the mirror equation holds for both concave and convex mirrors, for real and virtual images.
(E) In the Cartesian sign convention, distances measured opposite to the direction of the incident light are negative. — True. Distances along the incident light are positive. Distances against it are negative.
NCERT (2026-27):
Focal length of spherical mirrors – “Now, for small θ, the point D is very close to the point P. Therefore, FD = f and CD = R. … then gives”
\( \displaystyle f=R/2 \)\( \qquad (9.3) \)
Focal length of spherical mirrors – “… For a convex mirror, the reflected rays appear to diverge from a point F on its principal axis …”
The mirror equation – “(ii) The ray passing through the centre of curvature of a concave mirror or appearing to pass through it for a convex mirror. The reflected ray simply retraces the path.”
The mirror equation – “With the proper use of sign convention, these are, in fact, valid for all the cases of reflection by a spherical mirror (concave or convex) whether the image formed is real or virtual.”
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 …”