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An object is at distance of 20m from a convex lens of focal length 0.3m. The lens forms an image of the object moves away from the lens at a speed of 5m/s, the speed and direction of the image will be:

Option 1) 3.22 X 10^-3m/s towards the lens

Option 2) 1.16 X 10^-3m/s towards the lens

Option 3) 0.92 X 10^-3m/s away from the lens

Option 4) 2.62 X 10^-3m/s away from the lens

Answers (1)

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Relation between object and image velocity if object is moving along principal axis -

$\underset{V_{im}}{\rightarrow}$ $=$ $\frac{-v^{2}}{u^{2}}$ $\underset{V_{om}}{\rightarrow}$

$\underset{V_{im}}{\rightarrow}$ = $\underset{V_{i}}{\rightarrow}$ - $\underset{V_{m}}{\rightarrow}$

$\underset{V_{om}}{\rightarrow}$ = $\underset{V_{o}}{\rightarrow}$ - $\underset{V_{m}}{\rightarrow}$

- wherein

$\underset{V_{o}}{\rightarrow}$ = velocity of object

$\underset{V_{i}}{\rightarrow}$ = velocity of image

$\underset{V_{m}}{\rightarrow}$ = velocity of mirror

$\underset{V_{om}}{\rightarrow}$ = velocity of object w.r.t. mirror

$\underset{V_{im}}{\rightarrow}$ = velocity of image w.r.t. mirror

From lens formula

$\frac{1}{V}=\frac{1}{0.3}-\frac{1}{20}$

$\Rightarrow V=\frac{60}{197}$

$m=\frac{V}{u}=\frac{\frac{60}{197}}{20}$

Velocity of image w.r.to lens

$V_{I}=m^{2}V_{o}$

and directions is same as that of object

$V_{I}= (\frac{\frac{60}{197}}{20})^{2}\: \: 5$

$=1.16\times 10^{-3}m/s$ towards the lens.

Option 1)

3.22 X 10^-3 m/s towards the lens

Option 2)

$1.16 \times 10^{-3}m/s$ towards the lens

Option 3)

$0.92 \times 10^{-3}m/s$ away from the lens

Option 4)

$2.26 \times 10^{-3}m/s$ away from the lens

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