The code you've provided is a Python program that simulates the refraction of light and gravitational lensing around a black hole. The program uses matplotlib for plotting.
Here's an improved version of your code with some minor improvements:

#Copyright Daniel Harding - RomanAILabs

python



import numpy as np
import math
import matplotlib.pyplot as plt

def simulate_refraction():
    """
    Simulate the bending of light due to refraction.
    
    Plots the incident and refracted rays, along with the interface between the two media.
    """
    # Parameters (in scaled units)
    theta1 = 30  # Angle of incidence
    normal = np.array([0, -1])  # Normal vector

    # Refracted direction
    dir_refracted = np.sin(theta2) * np.cross(normal, [1, 0]) / np.linalg.norm(np.cross(normal, [1, 0])) + np.cos(theta2) * normal
    dir_refracted = -dir_refracted  # Adjust for downward propagation

    # Extend refracted ray
    intersect = (10, 0)
    ray_start = (0, 0)

    # Plot
    plt.figure(figsize=(8, 6))
    plt.plot([ray_start[0], intersect[0]], [ray_start[1], intersect[1]], 'b-', label='Incident Ray')
    plt.plot([intersect[0], (10 + dir_refracted[0]) * np.cos(-math.atan2(dir_refracted[1], -dir_refracted[0]))],
             [intersect[1] + 10 * dir_refracted[1]], 'g-', label='Refracted Ray')
    plt.axhline(0, color='gray', linestyle='--', label='Interface')
    plt.xlim(-15, 25)
    plt.ylim(-5, 5)
    plt.xlabel('X')
    plt.ylabel('Y')
    plt.title('Light Bending via Refraction (Snell''s Law)')
    plt.legend()
    plt.grid(True)
    plt.show()

def simulate_grav_lensing():
    """
    Simulate the bending of light due to gravitational lensing.
    
    Plots the curved path of a photon near a black hole.
    """
    # Parameters
    M = 1.4 * (2e30)  # Mass of central object in kg
    Rs = 3  # Schwarzschild radius

    # Initial conditions
    r = np.linspace(0, 10, 100)
    phi = np.pi / 6 + 0.01

    # Effective potential and angular momentum
    L = 1  # Conserved angular momentum (for unit energy)

    # Integrate geodesic (Euler method for simplicity)
    def integrand(r, phi):
        B = 1 - Rs / r
        dphi_dr = (L / (r**2)) / math.sqrt(1 / B - (L**2 / (c**2 * r**2)))
        return [dphi_dr]

    # Perform numerical integration
    from scipy.integrate import solve_ivp
    sol = solve_ivp(lambda t, y: integrand(y[0], y[1]), [0, 10], [0, phi], method='BDF', atol=1e-6)

    # Plot
    plt.figure(figsize=(8, 6))
    x = r * np.cos(phi)
    y = r * np.sin(phi)
    plt.plot(x, y, 'r-', label='Light Path')
    plt.scatter(0, 0, color='black', s=100, label='Black Hole')
    plt.axhline(0, color='gray', lw=0.5)
    plt.axvline(0, color='gray', lw=0.5)
    plt.xlim(-10, 20)
    plt.ylim(-10, 20)
    plt.xlabel('X (scaled)')
    plt.ylabel('Y (scaled)')
    plt.title('Light Bending via Gravitational Lensing (Geodesic Path)')
    plt.legend()
    plt.grid(True)
    plt.show()

if __name__ == "__main__":
    print("Running Refraction Demo...")
    simulate_refraction()
    print("\nRunning Gravitational Lensing Demo...")
    simulate_grav_lensing()