Question

The image behind a convex mirror (radius of curvature = 80 cm) is located 11 cm behind the mirror.

(a) Where is the object located?

(b) What is the magnification of the mirror?

(c) Is the image upright or inverted, relative to the object?

(d) Is the image larger or smaller than the object?

Answer 1

(a) First of all, we use the mirror equation for convex lens to find where the object is located;

$\frac{1}{f} = \frac{1}{o}+\frac{1}{i}$ , where f is the focal length, o is distance of object from the mirror, and i is the distance of image.

Since radius of curvature = 2(focal length), and focal length for a convex mirror is considered negative according to convention, therefore f = - 80/2 = - 40 cm

Given, i = - 11 cm (negative sign because the image is virtual)

Thus, $-\frac{1}{40} = \frac{1}{o}-\frac{1}{11}$

$\frac{1}{o} = \frac{1}{11} - \frac{1}{40}$

o = 15.2 cm

(b) Magnification = - i/o = - (-11)/15.2 = 0.72

(c) Since the magnification is positive, the image is upright.

(d) Since the magnification is less than 1, the image is smaller than the object.