Answer:
15 cm
Explanation:
[tex]h_{o}[/tex] = Diameter of the coin = 15 mm
[tex]h_{i}[/tex] = Diameter of the image of coin = 5 mm
[tex]d_{o}[/tex] = distance of the coin from mirror = 15 cm
[tex]d_{i}[/tex] = distance of the image of coin from mirror = ?
Using the equation
[tex]\frac{d_{i}}{d_{o}} = \frac{- h_{i}}{h_{o}}[/tex]
[tex]\frac{d_{i}}{15} = \frac{- (5)}{15}[/tex]
[tex]d_{i}[/tex] = - 5 cm
[tex]R[/tex] = radius of curvature
Using the mirror equation
[tex]\frac{1}{d_{o}} + \frac{1}{d_{i}} = \frac{2}{R}[/tex]
[tex]\frac{1}{15} + \frac{1}{- 5} = \frac{2}{R}[/tex]
[tex]R[/tex] = - 15 cm
