Draw a lens ray diagram with Python

A candle $3\ \text{cm}$ tall stands $20\ \text{cm}$ in front of a convex lens of focal length $8\ \text{cm}$. You will make the program find the image from the lens formula, find its height, and say if it is real or virtual. Then it draws two rays and the image.

The idea. With the signs, $u = -20\ \text{cm}$ and $f = +8\ \text{cm}$. Then $\dfrac{1}{v} = \dfrac{1}{f} + \dfrac{1}{u}$ and $h' = \dfrac{v}{u} \times h$.

Your tasks.

1. Work out v, the image distance, in cm.
2. Work out h_image, the height of the image, in cm.
3. Set kind to "real" or "virtual", from the sign of v.