Question

The ratio of the speed of an object to the speed of its real image of magnification \(m\) of a convex mirror is

• A. \(-\frac{1}{m^2}\)
• B. \(m^2\)
• C. \(-m\)
• D. \(\frac{1}{m}\)

Hint:

For convex mirror, image is virtual, but the formula holds for real images as well.

Answer 1

The Correct Option is A

Step 1: Concept:
Mirror formula: \(\frac{1}{f} = \frac{1}{v} + \frac{1}{u}\). Magnification \(m = -\frac{v}{u}\). Differentiate w.r.t time.
Step 2: Explanation:
\(\frac{1}{u} + \frac{1}{v} = \frac{1}{f}\). Differentiating: \(-\frac{1}{u^2}\frac{du}{dt} - \frac{1}{v^2}\frac{dv}{dt} = 0\).
\(\frac{du/dt}{dv/dt} = -\frac{u^2}{v^2} = -\frac{1}{m^2}\).
Thus, ratio of object speed to image speed = \(-\frac{1}{m^2}\).
Step 3: Conclusion:
Thus, ratio = \(-\frac{1}{m^2}\).