A mirror forms an image which is 30cm from an object and twice it… - Vidyadip

Question

A mirror forms an image which is 30cm from an object and twice its height.

Where must the mirror be situated?
What is the radius of curvature?
Is the mirror convex or concave?

✓

Answer

Let the image formed is virtual and erect.v - u = 30cm
m = 2

$\text{m}=-\frac{\text{v}}{\text{u}}$

$2=-\frac{\text{v}}{\text{u}}$
$\Rightarrow{\text{v}}=2{\text{u}}$
$2\text{u}-\text{u}=30\text{cm}$
$\text{u}=-10\text{cm}$

$\text{v}=-2\text{u}=20\text{cm}$

$\frac{1}{\text{v}}+\frac{1}{\text{u}}=\frac{1}{\text{f}}$
$\frac{1}{\text{f}}=\frac{-1}{20}$
$\text{f}=-20\text{cm}$
$\text{R}=2\text{f}=-40\text{cm}$

Concave mirror.

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