Question

An ant is 15 cm from the convex mirror of focal length 10 cm. If the ant starts to move towards the mirror with 0.5 m/s. Calculate the velocity of the image.

Answer 1

Magnitude of the velocity of image is 2 m/s

Step-by-step explanation:

As we know that the mirror's formula for convex lens,

`(1)/(v)+(1)/(u)= (1)/(f)`

Given that the ant is 15 cm from the convex mirror,

`u=15 cm`

And focal length of the mirror is,

`f=10 cm`

And the ant is moving towards the mirror,

`(du)/(dt)=0.5m/s`

Now calculate v,

`(1)/(v)= (1)/(10)-(1)/(15) \\(1)/(v)=(3-2)/(30) \\v=30 cm`

Now differentiate the mirror's formula with respect to t and in this focal length is constant.

`-(1)/(v^(2) )(dv)/(dt)-(1)/(u^(2) )(du)/(dt) =0\\ (dv)/(dt)=-(v^(2) )/(u^(2) ) (du)/(dt)`

Now put all the variables to get velocity of image,

`(dv)/(dt)=-((30)/(15))^(2) (0.5)\\(dv)/(dt)=4* 0.5\\(dv)/(dt)=-2 m/s`

Therefore, the velocity of image is -2 m/s negative sign means that the direction of velocity of image is opposite to direction of velocity of ant.