Question
An object moves towards a convex lens of focal length 20
cm with a velocity of 5 cm/s. When the object is at 30 cm from the lens, find the rate at which the image is moving.Solution
Given:
- Focal length of convex lens, f = +20 cm
- Object distance at a given instant, u = –30 cm (object is in front ⇒ negative in sign convention)
- Object velocity: du/dt = +5 cm/s (since it's moving towards the lens, u is decreasing ⇒ du/dt is positive)
dv/dt = ?, i.e., rate of change of image position. Using lens formula: 1/v – 1/u = 1/f Differentiate both sides with respect to time t :
The image is moving away from the lens at a rate of 20 cm/s.
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