Question:
A point object moves towards a concave mirror (f = 20 cm) at 4 cm/s. Find speed of image when object is at 60 cm.
A point object moves towards a concave mirror (f = 20 cm) at 4 cm/s. Find speed of image when object is at 60 cm.
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Use differentiation of mirror formula for velocity problems.
Updated On: Jun 17, 2026
- 3 cm/s
- 1 cm/s
- 2 cm/s
- 4 cm/s
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The Correct Option is C
Solution and Explanation
Step 1: Mirror formula: \[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \]
Step 2: Differentiate: \[ \frac{dv}{dt} = \left(\frac{v^2}{u^2}\right)\frac{du}{dt} \]
Step 3: Given: \[ f = -20,\quad u = -60,\quad \frac{du}{dt} = 4 \]
Step 4: Find v: \[ \frac{1}{-20} = \frac{1}{v} - \frac{1}{60} \Rightarrow v = -30 \]
Step 5: \[ \frac{dv}{dt} = \left(\frac{900}{3600}\right)4 = 2\ \text{cm/s} \]
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