18. A candle $3.0 \mathrm{~cm}$ high is placed $30 \mathrm{~cm}$ from a converging mirror with a focal length of $20 \mathrm{~cm}$. Using the mirror and magnification equations, determine the image position and its height.

Step 1 ：Given the object height \(h_o = 3 \mathrm{~cm}\), object distance \(d_o = 30 \mathrm{~cm}\), and focal length \(f = 20 \mathrm{~cm}\).

Step 2 ：Use the mirror equation to find the image distance \(d_i\): \(\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}\)

Step 3 ：Solve for \(d_i\): \(d_i = \frac{1}{\frac{1}{f} - \frac{1}{d_o}} = \frac{1}{\frac{1}{20} - \frac{1}{30}} \approx 60 \mathrm{~cm}\)

Step 4 ：Use the magnification equation to find the image height \(h_i\): \(M = -\frac{d_i}{d_o} = \frac{h_i}{h_o}\)

Step 5 ：Solve for \(h_i\): \(h_i = M \cdot h_o = -\frac{d_i}{d_o} \cdot h_o = -\frac{60}{30} \cdot 3 = -6 \mathrm{~cm}\)

Step 6 ：\(\boxed{\text{The image position is approximately 60 cm from the mirror, and the image height is approximately -6 cm (the negative sign indicates that the image is inverted).}}\)