The Young double-slit experiment | 杨氏双缝实验

📚 The Young double-slit experiment | 杨氏双缝实验

The Young double-slit experiment is a cornerstone of wave optics, demonstrating that light can interfere and therefore behaves as a wave. For A-Level Computer Science students, this experiment also offers an excellent opportunity to study computational modelling, numerical methods, and graphical simulation of a physical phenomenon.

杨氏双缝实验是波动光学的基石，证明了光可以发生干涉，因此具有波动性。对于 A-Level 计算机科学学生来说，这个实验还提供了一个极好的机会来研究物理现象的计算建模、数值方法和图形模拟。

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1. Historical context and significance | 历史背景与意义

Thomas Young conducted the double-slit experiment in 1801 to challenge Newton’s corpuscular theory of light. The pattern of alternating bright and dark fringes could only be explained if light travelled as waves that superimposed constructively and destructively.

托马斯·杨于 1801 年进行了双缝实验，以挑战牛顿的光的微粒说。交替出现的明暗条纹图样只有用光以波的形式传播并发生相长和相消叠加才能解释。

In computing, the experiment is an ideal candidate for simulation because its core mathematics can be discretised and rendered as an image. The same principles used to model interference patterns appear in signal processing, image analysis, and scientific computing.

在计算领域，该实验是模拟的理想对象，因为其核心数学可以离散化并渲染为图像。用于模拟干涉图样的相同原理也出现在信号处理、图像分析和科学计算中。

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2. Coherent light and experimental setup | 相干光与实验装置

The traditional setup uses a monochromatic light source, a barrier with two narrow slits separated by distance d, and a screen at distance D from the slits. The slits act as two coherent sources because they are illuminated by the same incident wavefront.

传统装置使用单色光源、一个带有间距为 d 的两条窄缝的挡板，以及一个距离狭缝为 D 的屏幕。两条狭缝作为两个相干光源，因为它们由同一入射波前照亮。

In a computational model, physical slits are replaced by two point sources. The model calculates the field contribution from each source at every pixel on the screen, then sums the contributions to obtain the resultant intensity.

在计算模型中，物理狭缝被两个点源取代。模型计算每个源在屏幕上每个像素处的场贡献，然后将贡献求和以获得合成强度。

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3. Path difference and the interference equation | 光程差与干涉方程

At a point P on the screen with vertical coordinate y, the waves from the two slits travel different distances. For small angles, the path difference is approximated by:

在屏幕上垂直坐标为 y 的点 P 处，来自两条狭缝的波传播的距离不同。对于小角度，光程差近似为：

Δr = d sin θ ≈ d × y / D

Bright fringes appear when the path difference equals an integer number of wavelengths: Δr = mλ, where m = 0, ±1, ±2, … Dark fringes occur when Δr = (m + ½)λ. The distance between adjacent bright fringes is therefore:

当光程差等于整数个波长时出现亮条纹：Δr = mλ，其中 m = 0, ±1, ±2, … 当 Δr = (m + ½)λ 时出现暗条纹。因此相邻亮条纹之间的距离为：

Δy = λD / d

This fringe spacing equation is central to the experiment and provides a simple way to validate any computer simulation against analytical results.

该条纹间距方程是实验的核心，并提供了将任何计算机模拟与解析结果进行验证的简单方法。

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4. Intensity distribution and fringe pattern | 强度分布与条纹图样

The intensity at point P is determined by the phase difference δ between the two waves. The phase difference is related to the path difference by δ = 2π Δr / λ. The resulting intensity is proportional to the square of the cosine of half the phase difference.

点 P 处的强度由两列波之间的相位差 δ 决定。相位差与光程差的关系为 δ = 2π Δr / λ。由此产生的强度与半相位差的余弦平方成正比。

I = I₀ cos²(π d y / (λ D))

This formula predicts equally spaced bright and dark bands. In a computational approach, the intensity can be calculated directly for each pixel using this expression, avoiding the need to solve a full wave equation.

该公式预测了等间距的明暗条纹。在计算方法中，可以使用该表达式直接为每个像素计算强度，而不需要求解完整的波动方程。

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5. Why simulate the double-slit experiment | 为什么要模拟双缝实验

Simulating the double-slit experiment is a common project in computer science because it links numerical computation, algorithmic design, and graphical output. Students can change parameters such as wavelength or slit separation and observe effects immediately, which is often impossible in a physical laboratory.

模拟双缝实验是计算机科学中一个常见的项目，因为它将数值计算、算法设计和图形输出联系起来。学生可以更改波长或狭缝间距等参数并立即观察效果，这在物理实验室中通常是不可能的。

From a computational perspective, the task is to map a 2D array of screen coordinates to intensity values using the interference formula. This requires careful discretisation, floating-point arithmetic, and an efficient rendering pipeline.

从计算角度看，任务是使用干涉公式将屏幕坐标的二维阵列映射为强度值。这需要仔细的离散化、浮点运算和高效的渲染流程。

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6. Building a computational grid | 构建计算网格

The screen is represented as a two-dimensional grid with Nx columns and Ny rows. Each grid cell corresponds to a small area on the screen, and its centre coordinates (x, y) are used in calculations. If the screen has physical width W and height H, the pixel spacing is dx = W / Nx and dy = H / Ny.

屏幕被表示为一个二维网格，具有 Nx 列和 Ny 行。每个网格单元对应屏幕上的一个小区域，其中心坐标 (x, y) 用于计算。如果屏幕的物理宽度为 W、高度为 H，则像素间距为 dx = W / Nx 和 dy = H / Ny。

Resolution selection affects both image quality and execution time. A grid of 800 × 600 pixels is usually sufficient for visual inspection, while 1920 × 1080 produces finer detail but requires more computational resources.

分辨率的选择会影响图像质量和执行时间。800 × 600 像素的网格通常足以进行视觉检查，而 1920 × 1080 能产生更精细的细节，但需要更多的计算资源。

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7. Computing intensity numerically | 数值计算强度

For each pixel at coordinate (x, y), the distances to the two slit positions are calculated. If the slits are located at (-d/2, 0) and (+d/2, 0) in the slit plane, and the screen is at z = D, the two distances are:

对于位于坐标 (x, y) 的每个像素，计算其到两个狭缝位置的距离。如果狭缝位于狭缝平面中的 (-d/2, 0) 和 (+d/2, 0)，屏幕位于 z = D，则两个距离为：

r₁ = √((x + d/2)² + y² + D²)

r₂ = √((x – d/2)² + y² + D²)

The path difference is Δr = r₂ – r₁, and the intensity is I = cos²(π Δr / λ). This direct method avoids the small-angle approximation and is more accurate for large y values, but it is more computationally expensive due to the square-root operations.

光程差为 Δr = r₂ – r₁，强度为 I = cos²(π Δr / λ)。这种直接方法避免了小角度近似，并且对于较大的 y 值更准确，但由于平方根运算，计算成本更高。

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8. Rendering the interference pattern | 渲染干涉图样

After all intensities have been computed, the values must be mapped to a displayable format. A greyscale image can be produced by multiplying the intensity by 255 and rounding to the nearest integer. A colour map such as ‘hot’ or ‘viridis’ can reveal subtle variations in brightness more effectively.

在计算完所有强度之后，必须将这些值映射为可显示的格式。灰度图像可以通过将强度乘以 255 并四舍五入到最接近的整数来生成。’hot’ 或 ‘viridis’ 等颜色映射可以更有效地显示亮度的细微变化。

When displayed, the central bright fringe should appear at y = 0, and

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