Answer:
R = 40 cm
Explanation:
From the formulae of magnification:
[tex]\frac{q}{p}=\frac{image\ height}{object\ height}\\\\\frac{q}{10\ cm} = \frac{4\ cm}{2\ cm}\\\\q = (10\ cm)(2)\\\\q = 20\ cm[/tex]
where,
q = image distance from mirror
p = object distance from mirror
Using thin lens formula:
[tex]\frac{1}{f}=\frac{1}{p}+\frac{1}{q}\\\\\frac{1}{f}=\frac{1}{10\ cm}+\frac{1}{-20\ cm}\\\\\frac{1}{f} = 0.05\\\\f = 20\ cm[/tex]
q is negative for the virtual image.
Now, the radius of the spherical mirror is double the focal length (f):
R = 2f
R = 2(20 cm)
R = 40 cm
