A point object moves towards a convex mirror with a constant speed.Prove that the speed of the image increases as the object comes closer to the mirror.

According to mirror formula
\[\begin{align}\frac{1}{v}+\frac{1}{u}&=\frac{1}{f}\\\left(\frac{-1}{{v}^2}\right){v}_{i}+\left(\frac{-1}{{u}^2}\right){v}_{o}&=0\\{v}_{i}&=-{\left(\frac{v}{u}\right)}^2{v}_{o}\\\huge\color{blue}{\boxed{{v}_{i}=-{m}^2{v}_{o}}}\end{align}\]
Since magnification of an object approaching towards mirror increases, the speed of image increases.

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TopNewestAccording to mirror formula

\[\begin{align}\frac{1}{v}+\frac{1}{u}&=\frac{1}{f}\\\left(\frac{-1}{{v}^2}\right){v}_{i}+\left(\frac{-1}{{u}^2}\right){v}_{o}&=0\\{v}_{i}&=-{\left(\frac{v}{u}\right)}^2{v}_{o}\\\huge\color{blue}{\boxed{{v}_{i}=-{m}^2{v}_{o}}}\end{align}\] Since magnification of an object approaching towards mirror increases, the speed of image increases.

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Thanks a lot!

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@Aditya Kumar @Surya Prakash

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U just have to differentiate the main equation wrt time.

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Yeah.Thanks.

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