Answer:
The focal length is [tex]f = -0.2 \ m[/tex]
The radius of curvature is [tex]R = -0.4 \ m[/tex]
Explanation:
From the question we are told that
The magnification of the mirror is [tex]m = \frac{1}{2}[/tex]
The distance of the person from the mirror(the object distance ) is [tex]u = - 1.0 \ m[/tex]
The negative sign shows that it is been placed in front of the mirror
Generally the magnification of the mirror is mathematically represented as
[tex]m = \frac{v}{u}[/tex]
=> [tex]\frac{1}{4} = \frac{v}{-u}[/tex]
=> [tex]v = \frac{- 1}{4}[/tex]
Generally from the lens equation we have that
[tex]\frac{1}{f} = \frac{1}{u} + \frac{1}{v}[/tex]
=> [tex]\frac{1}{f} = \frac{1}{-1 } + \frac{1}{-\frac{1}{4} }[/tex]
=> [tex]f = -0.2 \ m[/tex]
Generally the radius of curvature is mathematically represented as
[tex]R = 2 * f[/tex]
=> [tex]R = 2 * - 0.2[/tex]
=> [tex]R = -0.4 \ m[/tex]
