Question

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).

Answer 1

Answer:

The focal length is   $f = -0.2 \ m$

The radius of curvature is $R = -0.4 \ m$

Explanation:

From the question we are told that

       The magnification of the mirror is  $m = \frac{1}{2}$

       The distance of the person from the mirror(the object distance ) is  $u = - 1.0 \ m$

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

         

Generally the magnification of the mirror is mathematically represented as

       $m = \frac{v}{u}$

=>   $\frac{1}{4} = \frac{v}{-u}$

=>   $v = \frac{- 1}{4}$

Generally from the lens equation we have that

        $\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$

=>     $\frac{1}{f} = \frac{1}{-1 } + \frac{1}{-\frac{1}{4} }$

=>     $f = -0.2 \ m$

Generally the radius of curvature is  mathematically represented as

         $R = 2 * f$

=>      $R = 2 * - 0.2$

=>      $R = -0.4 \ m$