Microscopes and telescopes in code

You will write three functions about instruments that make things look larger and about the limit of what they can show.

The idea. A magnifying glass of focal length $f$ has $m = 1 + \dfrac{D}{f}$ when the image is at the near point and $\dfrac{D}{f}$ when it is at infinity, with $D = 25\ \text{cm}$. A compound microscope with the final image at infinity has $|M| = \dfrac{L}{f_o}\cdot\dfrac{D}{f_e}$. A telescope with an objective of diameter $D$ separates two points only if the angle between them is at least $\theta = \dfrac{1.22\,\lambda}{D}$. One radian is $\dfrac{180}{\pi}$ degrees, and one degree is $3600$ arcseconds.

Your tasks.

1. In simple_magnification, return the magnifying power. The argument at_near_point is True or False.
2. In compound_magnification, return the size of the magnifying power of the microscope.
3. In smallest_angle, return the smallest angle in arcsecond. The wavelength is in nm and the aperture is in m.