A student places an object 10cm in front of two different spherical mirrors:
Mirror A: convex, focal length +15cm
Mirror B: concave, focal length −15cm (signs as per Cartesian convention)
Treat the object and both mirrors to be coaxial and obey the small-angle (paraxial) approximation.
(i) For each mirror, derive an algebraic expression for the image distance in terms of the given object distance and focal length, clearly indicating the sign of every quantity used.
(ii) Calculate the numerical value of the image distance for Mirror A and for Mirror B.
(iii) For each mirror, compute the linear magnification and state whether the image is real or virtual, erect or inverted, enlarged or diminished.
(iv) Determine the ratio of the absolute sizes of the two images (convex to concave).
(v) Based on your results, explain why convex mirrors, and not concave mirrors, are fitted as rear-view mirrors on vehicles.