在我们的日常生活中，常常会遇到一些令人惊叹的天气奇观，如彩虹、极光、海市蜃楼等。这些现象不仅美丽壮观，更蕴含着丰富的科学知识。今天，就让我们一起来揭秘这些大自然奇妙现象背后的科学奥秘。

彩虹：光的色散与折射

彩虹是大气中的一种光学现象，当太阳光穿过雨滴时，会发生折射、反射和再次折射。由于不同颜色的光具有不同的波长，因此在折射过程中，它们会被分散成不同的颜色，形成彩虹。

代码示例：模拟彩虹形成过程

import matplotlib.pyplot as plt
import numpy as np

# 定义折射角度
angle = 42

# 定义光的波长
wavelengths = np.array([400, 540, 590, 620, 650, 700])  # 红橙黄绿蓝靛紫

# 计算折射角度
refracted_angles = np.arcsin(np.sin(np.radians(angle)) / wavelengths / (1 - np.cos(np.radians(angle))))

# 绘制彩虹
plt.figure(figsize=(10, 5))
plt.plot(wavelengths * 1e-9, np.degrees(refracted_angles), marker='o')
plt.title('彩虹形成过程')
plt.xlabel('波长 (nm)')
plt.ylabel('折射角度 (°)')
plt.grid(True)
plt.show()

极光：太阳风与地球磁场

极光是一种发生在地球高纬度地区的自然现象，由太阳风中的带电粒子进入地球磁场并与大气层中的气体相互作用产生。极光分为北极光和南极光，分别发生在北极和南极地区。

代码示例：模拟极光形成过程

import numpy as np
import matplotlib.pyplot as plt

# 定义地球磁场方向
B = np.array([0, 1, 0])

# 定义太阳风带电粒子方向
v = np.array([1, 0, 0])

# 计算粒子进入地球磁场后的运动轨迹
theta = np.arccos(np.dot(B, v) / np.linalg.norm(B))
phi = np.linspace(0, 2 * np.pi, 100)
r = np.linalg.norm(B) * np.sin(theta) * np.cos(phi)
z = np.linalg.norm(B) * np.sin(theta) * np.sin(phi)

# 绘制极光
plt.figure(figsize=(10, 5))
plt.plot(r, z, color='blue')
plt.title('极光形成过程')
plt.xlabel('径向距离')
plt.ylabel('高度')
plt.grid(True)
plt.show()

海市蜃楼：光的折射与全反射

海市蜃楼是一种由于大气折射和全反射现象而产生的视觉错觉。当光线从密度较低的大气层进入密度较高的大气层时，会发生折射。如果入射角大于临界角，光线会发生全反射，从而形成海市蜃楼。

代码示例：模拟海市蜃楼形成过程

”`python import numpy as np import matplotlib.pyplot as plt

定义大气层密度

density = np.array([1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225, 1.225,