First slide

The lens

Question

In the diagram shown, the lens is moving towards the object with a velocity V m/s and the object is also moving towards the lens with the same speed. What is speed of the image with respect to earth when the object is at a distance 2f from the lens?
(f is the focal length):

Moderate

A

2 V
B

4 V
C

3 V
D

V

Solution

$\begin{array}{l} V_{il} = {(\frac{v}{u})}^{2} (V_{o / l}) \\ V_{i} - V_{l} = {(\frac{+ 2 f}{- 2 f})}^{2} (V_{0} - V_{l}) \\ V_{i} - (- V) = (- 1)^{2} [V - (- V)] \\ \Rightarrow V_{i} = V \end{array}$

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