Question

an object is 30 cm awayfrom a convex mirror. the image is 6 cm awayfrom the mirror is the image real or virtual? what is the focal length of the mirror? what is the radius of the mirror? if the objectis .25 cm of height what is the image size? what is the magnification?

Answer 1

Convex mirror always produces virtual images.

Given is:-

Object is located 30 cm away from the mirror, image is 6 cm away from the mirror.

we know that for spherical mirrors

where u is the distace of object from the mirror, v is distace of the object and R is the radius of curvature of the mirror.

By taking cartesian convetions, we get

by putting these values in above equation, we get

Thus the Radius of curvature of the given spherical convex mirror is 15cm

we also know that the focal length of mirror is

THus the the focal length of the given mirror is f=7.5cm

Using a ray parallel to the principal axis and one incident upon the center of the mirror, the position of the image can be constructed by back-projecting the rays which reflect from the mirror. The virtual image that is formed will appear smaller and closer to the mirror than the object.

The lateral magnification is defined as the ratio of the height of image over the height of the object

For a convex mirror

h2 is the height of the image where h1 is the height of the object and m is lateral magnification

by putting all the values in above equation, we get

Thus the height of the image is 0.05 cm

and magnification is