Question

if f=40cm in convex mirror, and image is half the size of image, find image distance

Answer 1

20 cm

Answer 2

For a convex mirror, the focal length $f = +40 \text{ cm}$. The magnification $m = +1/2$ because the image is half the size and formed by a convex mirror (virtual and erect). Using the magnification formula $m = -v/u$, we get $1/2 = -v/u$, which implies $u = -2v$. Substituting this into the mirror formula $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$, we get $\frac{1}{v} + \frac{1}{-2v} = \frac{1}{40}$. Simplifying this equation gives $\frac{1}{2v} = \frac{1}{40}$, which yields $2v = 40$, so $v = 20 \text{ cm}$.