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Velocity of a point is  v_{0}=2 \mathrm{cm} / \mathrm{s} when it is placed at a distance of 30 cm from a lens moving with a speed v_{\mathrm{lens}}=2 \mathrm{cm} / \mathrm{s} towards left. If the focal length of the lens is f=20 \mathrm{cm}, find the velocity of the image.

                                 

Option: 1

14 cm/s in left direction


Option: 2

14 cm/s in right direction


Option: 3

7 cm/s in left direction


Option: 4

7 cm/s in right direction


Answers (1)

best_answer

 

 

 

Velocity of image w.r.t. lens along the principal axis is given by

\begin{array}{l}{\quad \vec{V}_{\text {image },\text {lens }}=m^{2} \vec{V}_ \text { object, lens }} \\ \\ {\Rightarrow \quad\left(\vec{V}_{\text {image }}-\vec{V}_{\text {lens }}\right)=\left(\frac{v}{u}\right)^{2}\left(\vec{V}_{\text {object }}-\vec{V}_{\text {lens }}\right)} \\ \\ {\text { Using: } \frac{1}{v}-\frac{1}{u}=\frac{1}{f} \Rightarrow \frac{1}{v}-\frac{1}{(-30)}=\frac{1}{(+20)} \Rightarrow v=+60 \mathrm{cm}}\end{array}

\vec{V}_{\text {inver }}=\left(\frac{+60}{-30}\right)^{2}[(2 \hat{i})-(-2 \hat{i})]+(-2 \hat{i})=14 \hat{i} \mathrm{cm} / \mathrm{s}

It means that the velocity is 14 cm/s in the right direction.

Posted by

jitender.kumar

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