Lenses in code

You will write three small functions about thin lenses.

The idea. In the New Cartesian convention a real object has a negative distance $u$. The thin lens formula is $\dfrac{1}{v} - \dfrac{1}{u} = \dfrac{1}{f}$. Two lenses a gap $d$ apart have the power $P = P_1 + P_2 - dP_1P_2$, with $d$ in metre. The lens maker's formula is $\dfrac{1}{f} = (n-1)\left(\dfrac{1}{R_1} - \dfrac{1}{R_2}\right)$. A flat face has an infinite radius.

Your tasks.

1. In image_distance, return the image distance $v$ from $u$ and $f$.
2. In pair_power, return the power of two lenses in dioptre, with the gap in metre.
3. In focal_length, return the focal length from $n$, $R_1$ and $R_2$.