Question

Convex mirrors allow for a wide view, which is why they are used as security mirrors in stores.

(a) Draw the ray diagram for an object being reflected in a convex mirror. Use the ray through the centerline and the ray that comes parallel to the mirror.

(b) The books goes through the proof of the relationship between a source location, s, the image location, i, and the focal length, f, given by:

1/s + 1/s' = 1/f .

Prove that this relation holds for a convex mirror

Answer 1

a). We know that Convex Mirror has negative focal length. Thus ray diagram will be

b). Using Equation of Mirrors,

  

Now for mirrors, focal length is always negative and object is always real and positive. Then we'll have

Hence always. (Means image is formed right to the mirror hence virtual)

Hence for convex mirror, for any object distance, Image will be always virtual which we can see from above ray diagram also. Hence this relation holds for a convex mirror.