convex mirror

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.

Easy Math Editor

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Comments

According to mirror formula
$\begin{aligned}\frac{1}{v}+\frac{1}{u}&=\frac{1}{f}\\\left(\frac{-1}{{v}^2}\right){v}_{i}+\left(\frac{-1}{{u}^2}\right){v}_{o}&=0\\{v}_{i}&=-{\left(\frac{v}{u}\right)}^2{v}_{o}\\\huge\color{#3D99F6}{\boxed{{v}_{i}=-{m}^2{v}_{o}}}\end{aligned}$ Since magnification of an object approaching towards mirror increases, the speed of image increases.

Rohit Ner - 5 years, 6 months ago

Thanks a lot!

Adarsh Kumar - 5 years, 6 months ago

@Aditya Kumar @Surya Prakash

Adarsh Kumar - 5 years, 6 months ago

U just have to differentiate the main equation wrt time.

Aditya Kumar - 5 years, 6 months ago

Yeah.Thanks.

Adarsh Kumar - 5 years, 6 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$