def design_symmetric_compound_lens(f, w):
    """Design a compound lens with a given focal length and working distance.

    Args:
       f: Desired focal length.
       w: Desired working distance, defined here as distance from focal planes to the outer principal planes of the singlets.

    Returns:
        fl: Focal length of singlet.
        d: Separation of inner principal planes of singlets.
    """
    # This turns out to be true... I derived it algebraically. There should be geometric argument but I can't think of one
    # right now.
    fl = w + f
    d = (f**2 - w**2)/f
    return fl, d