Explanation:
Given that,
Height of object = 4.31 cm
Distance of the object = -12.6 cm
Distance of the image = -8.77 cm
For concave mirror,
Using mirror's formula
[tex]\dfrac{1}{f}=\dfrac{1}{u}+\dfrac{1}{v}[/tex]
[tex]\dfrac{1}{f}=\dfrac{1}{-12.6}-\dfrac{1}{8.77}[/tex]
[tex]\dfrac{1}{f}=-\dfrac{10685}{55251}[/tex]
[tex]f=-\dfrac{55251}{10685}[/tex]
[tex]f = -5.17\ cm[/tex]
Radius of the mirror is
[tex]f = |\dfrac{R}{2}|[/tex]
[tex]r=2f[/tex]
[tex]r=2\times5.17[/tex]
[tex]r=10.34\ cm[/tex]
The magnification of the mirror,
[tex]m=-\dfrac{v}{u}[/tex]
[tex]\dfrac{h_{i}}{h_{o}}=\dfrac{v}{u}[/tex]
[tex]h_{i}=-h_{o}\times\dfrac{v}{u}[/tex]
[tex]h_{i}=-4.31\times\dfrac{8.77}{12.6}[/tex]
[tex]h_{i}=-2.99\ cm[/tex]
Now, For convex mirror,
Using mirror's formula
[tex]\dfrac{1}{f}=\dfrac{1}{u}+\dfrac{1}{v}[/tex]
[tex]\dfrac{1}{f}=\dfrac{1}{-12.6}+\dfrac{1}{8.77}[/tex]
[tex]\dfrac{1}{f}=\dfrac{1915}{55251}[/tex]
[tex]f=\dfrac{55251}{1915}[/tex]
[tex]f = 28.85\ cm[/tex]
Radius of the mirror is
[tex]f = \dfrac{R}{2}[/tex]
[tex]r=2f[/tex]
[tex]r=2\times28.85[/tex]
[tex]r=57.7\ cm[/tex]
The magnification of the mirror,
[tex]m=-\dfrac{v}{u}[/tex]
[tex]\dfrac{h_{i}}{h_{o}}=\dfrac{v}{u}[/tex]
[tex]h_{i}=-h_{o}\times\dfrac{v}{u}[/tex]
[tex]h_{i}=4.31\times\dfrac{8.77}{12.6}[/tex]
[tex]h_{i}=2.99\ cm[/tex]
Hence, This is the required solution.