单缝衍射python
时间: 2025-01-11 22:53:25 浏览: 72
### 使用Python实现单缝衍射实验仿真
为了在Python中实现单缝衍射仿真实验,可以采用夫琅和费衍射理论中的单缝衍射光强公式。该公式的表达形式如下:
\[ I(\theta)=I_0\left[\frac{\sin \beta}{\beta}\right]^2,\quad \text{其中}~\beta=\pi a \sin\theta/\lambda \]
这里 \(a\) 是狭缝宽度,\(λ\) 表示入射光波长,而 \(θ\) 则是从中心轴到观察点的角度位置[^1]。
对于编程实践部分,在Python环境中可以通过`numpy`库来完成必要的数值运算,并利用`matplotlib.pyplot`来进行图形化展示。下面给出一段简单的代码用于绘制单缝衍射强度分布图:
```python
import numpy as np
import matplotlib.pyplot as plt
def single_slit_diffraction_intensity(x, wavelength=500e-9, slit_width=1e-6):
beta = np.pi * slit_width * np.sin(np.arctan(x / 1)) / wavelength
# Avoid division by zero error at the center of pattern (x=0)
intensity = np.zeros_like(beta)
nonzero_mask = beta != 0
intensity[nonzero_mask] = ((np.sin(beta[nonzero_mask]) / beta[nonzero_mask])**2)
# Central maximum is defined to be equal to 1 for normalization purposes.
if not all(nonzero_mask):
intensity[~nonzero_mask] = 1
return intensity
# Define parameters and generate data points
wavelength = 500e-9 # Wavelength in meters
slit_width = 1e-6 # Slit width in meters
screen_distance = 1 # Distance from slit to screen in meters
pixel_size = 1e-6 # Size of each pixel on detector plane in meters
num_pixels = 1000 # Number of pixels across detection area
positions = np.linspace(-num_pixels/2, num_pixels/2, num=num_pixels)*pixel_size*screen_distance
intensities = single_slit_diffraction_intensity(positions, wavelength=wavelength, slit_width=slit_width)
plt.figure(figsize=(8, 6))
plt.plot(positions*1e6, intensities) # Convert position units back into micrometers for better readability
plt.title('Single Slit Diffraction Intensity Distribution')
plt.xlabel(r'Position ($\mu$m)')
plt.ylabel('Normalized Intensity')
plt.grid(True)
plt.show()
```
这段程序定义了一个函数 `single_slit_diffraction_intensity()` 来计算给定位置处的相对光强值,并通过调用此函数生成一系列数据点以描绘出整个屏幕上的亮度变化情况。最后使用 Matplotlib 库将这些数据可视化出来形成直观的衍射图案[^2]。
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