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A mirror of radius of curvature 20cm and...

A mirror of radius of curvature 20cm and an object which is placed at a distance of 15cm are both moving with velocities `1ms^(-1)` and `10ms^(-1)` as shown in Fig. Fing the velocity of image at this situation.

Text Solution

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Using `1/v+1/u=2/R,` we get
`1/v-1/(15)=-1/(10)rArr v=-30cm`
Now, using `V_(im) = -(v^(2))/(u^(2))V_(OM)`
`(V_(i)-v_(m))=-(v^(2))/(u^(2))(V_(o)-V_(m))`
`rArr V_(i)-(1)=-((-30)^(2))/((-15)^(2))[(-10)-(1)]`
`rArr V_(i)=45cm s^(-1)`
So, the image will move with veloxity `45 cms^(-1)`.
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