Answer:
i = -12.7 cm; h = 5.07 cm
Explanation:
1. Find the focal length
The focal length of a concave spherical mirror is half of its radius of curvature.
f = ½r = ½ × 34.0 cm = 17.0 cm
2. Find the image distance
A convex mirror produces a virtual image behind the mirror, so the image distance is negative.
[tex]\begin{array}{rcl}\dfrac{1}{o} + \dfrac{1 }{i} & = & \dfrac{1}{f}\\\\\dfrac{1}{50.0} + \dfrac{1 }{i} & = & \dfrac{1}{-17.0}\\\\\dfrac{1}{i} & = & \dfrac{1}{-17.0} - \dfrac{1}{50.0}\\\\& = & \dfrac{50.0 - (-17.0)}{500\times(-17.0)}\\\\& = & \dfrac{67.0}{-850}\\\\i & = & \dfrac{-850}{67.0}\\\\& = & \textbf{-12.7 cm}\\\end{array}[/tex]
3. Find the image size
[tex]\begin{array}{rcl}\\\\\dfrac{h_{\text{i}}}{ h_{\text{o}}} & = & -\dfrac{i}{o} \\\\\dfrac{h_{\text{i}}}{ 20.0} & = & -\dfrac{-12.7}{50.0} \\\\h_{\text{i}} & = & 20.0 \times \dfrac{12.7}{50.0}\\\\& = & \textbf{5.07 cm}\\\end{array}[/tex]
