Question:
The ratio of the speed of an object to the speed of its real image of magnification \(m\) of a convex mirror is
The ratio of the speed of an object to the speed of its real image of magnification \(m\) of a convex mirror is
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For convex mirror, image is virtual, but the formula holds for real images as well.
Updated On: Apr 23, 2026
- \(-\frac{1}{m^2}\)
- \(m^2\)
- \(-m\)
- \(\frac{1}{m}\)
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept:
Mirror formula: \(\frac{1}{f} = \frac{1}{v} + \frac{1}{u}\). Magnification \(m = -\frac{v}{u}\). Differentiate w.r.t time.
Step 2: Detailed 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: Final Answer:
Thus, ratio = \(-\frac{1}{m^2}\).
Mirror formula: \(\frac{1}{f} = \frac{1}{v} + \frac{1}{u}\). Magnification \(m = -\frac{v}{u}\). Differentiate w.r.t time.
Step 2: Detailed 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: Final Answer:
Thus, ratio = \(-\frac{1}{m^2}\).
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