When you look at yourself in a convex mirror, you appear to be ¼ your actual size. If you are standing 1.0 m in front of the mirror, what is the mirror’s focal length and radius of curvature. (Be sure to first sketch the situation).

The focal length is  

The radius of curvature is

Explanation:

From the question we are told that

       The magnification of the mirror is  

       The distance of the person from the mirror(the object distance ) is  

        The negative sign shows that it is been placed in front of the mirror

Generally the magnification of the mirror is mathematically represented as

=>  

=>  

Generally from the lens equation we have that

=>    

=>    

Generally the radius of curvature is  mathematically represented as

=>      

=>