How far from the mirror surface is the image in the following case:Convex mirrors are used in stores to provide a wide angle of surveillance for a...

The focal length of a convex mirror is half the length of
its radius of curvature. Here the radius of curvature is given as 1 m. This gives the
focal length as 0.5 m.

The relation between the focal
length f, the distance of the object from the mirror Do and the distance of the image Di
from the mirror for a convex mirror is (1/f) = (1/Do) +
(1/Di).

We are given that the customer is 6 m away from the
mirror, Do = 6.

Substituting the values in the equation
given earlier:

1/-0.5 = 1/6 +
1/Di

=> 1/Di = 1/-0.5 -
1/6

=> -2 -
1/6

=> -13/6

=>
-2.167 m

The image of the customer is 2.167 m away from the
surface of the mirror.

As the distance of the image is
negative we know that it is a virtual image. A convex mirror always forms a virtual
image that is smaller than the object.