Lens experiments in code

You will write three small functions about the displacement method and lenses in other media.

The idea. The displacement method gives $f = \dfrac{D^2 - d^2}{4D}$. In a liquid, $f_m = f_{air}\dfrac{n_l - 1}{n_l/n_m - 1}$. A thin lens with the index $n_1$ on its left and $n_3$ on its right has $P = \dfrac{n_g - n_1}{R_1} + \dfrac{n_3 - n_g}{R_2}$ and $\dfrac{n_3}{v} = \dfrac{n_1}{u} + P$. All lengths are in centimetre.

Your tasks.

1. In bessel_focal_length, return the focal length in centimetre.
2. In focal_length_in_medium, return the focal length of the lens in the liquid.
3. In image_distance, return the distance $v$ of the image for a lens with different media on its two sides.