A convex mirror of radius of curvature 30 cm forms an image that is half the size of the object. The object distance is

Question

A convex mirror of radius of curvature 30 cm forms an image that is half the size of the object. The object distance is [2024]

Smart Achievers · Accepted Answer

(1)

Given R = 30 cm

$\Rightarrow f = \frac{R}{2} = + 15 c m$

Magnification (m) = $\pm 1 / 2$

For convex mirror, virtual image is formed for real object, therefore, $m$ is +ve

The mirror formula,

$\frac{1}{v} + \frac{1}{u} = \frac{1}{f} \Rightarrow v = \frac{u f}{u - f}$

Magnification, $m = - \frac{v}{u} = - \frac{u f}{u (u - f)} = \frac{f}{f - u}$

$\frac{1}{2} = \frac{f}{f - u} = \frac{15}{15 - u} \Rightarrow u = - 15 c m$

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