def lensmakers_equation(r1: float, r2: float, n_lens: float, thickness: float) -> float:
    """
    Calculate the focal length of a thick spherical lens using the lensmaker's equation.

    :param r1: the first radius of curvature, positive for convex, negative for concave
    :param r2: the second radius of curvature, negative for convex, positive for concave
    :param n_lens: the refractive index of the lens
    :param thickness: The thickness of the lens

    :return: The focal length of the lens based on the paraxial approximation
    """

    p = (n_lens - 1) * (1 / r1 - 1 / r2 + (n_lens - 1) * thickness / (n_lens * r1 * r2))
    return 1 / p