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

Accepted Answer

Given: A convex mirror has radius of curvature $R = 30 \, \text{cm}$ , so its focal length is

f = \frac{R}{2} = 15 \, \text{cm}

For a convex mirror, $f$ is positive in the Cartesian sign convention used for mirrors. The image is half the size of the object, so magnification is

m = \frac{1}{2}

Find: The object distance $u$ .

Using the mirror magnification relation,

m = -\frac{v}{u}

So,

\frac{1}{2} = -\frac{v}{u}

which gives

v = -\frac{u}{2}

Now use the mirror formula,

\frac{1}{f} = \frac{1}{v} + \frac{1}{u}

Substituting $f = 15$ and $v = -\frac{u}{2}$ ,

\frac{1}{15} = \frac{1}{-u/2} + \frac{1}{u}

\frac{1}{15} = -\frac{2}{u} + \frac{1}{u} = -\frac{1}{u}

Hence,

u = -15 \, \text{cm}

Therefore, the correct option is A.

Answer