🔦 折射角计算器（斯涅尔定律，含常见介质）Angle of Refraction Calculator (Law of Refraction, Common Media)

使用说明与常见问题How-to & FAQ

「折射角计算器（斯涅尔定律，含常见介质）」是什么？What is the Angle of Refraction Calculator (Law of Refraction, Common Media) tool?

选择或填写两种介质的折射率和入射角，用 n₁ sin θ₁ = n₂ sin θ₂ 求折射角，并给出偏折角、临界角和是否发生全反射。本地处理。Pick or type the refractive indices of the two media and the angle of incidence to get the angle of refraction from n₁ sin θ₁ = n₂ sin θ₂, plus the deviation, the critical angle and whether total internal reflection happens. Processed locally.

如何使用「折射角计算器（斯涅尔定律，含常见介质）」？How do I use the Angle of Refraction Calculator (Law of Refraction, Common Media) tool?

在「折射角计算器（斯涅尔定律，含常见介质）」中，填写「入射介质」、「自定义 n₁」、「折射介质」、「自定义 n₂」、「入射角（与法线夹角，度）」等参数，结果会随输入实时计算并显示在下方。In the Angle of Refraction Calculator (Law of Refraction, Common Media): Fill in "First medium", "Custom n₁", "Second medium", "Custom n₂", "Angle of incidence (from normal, degrees)"; results are recalculated instantly as you type.

角度从哪里量？Where is the angle measured from?

入射角和折射角都从法线（垂直于界面的线）量起，不是从界面本身量起。垂直入射时为 0°。Both angles are measured from the normal (the line perpendicular to the surface), not from the surface. Straight-on incidence is 0°.

什么时候会全反射？When does total internal reflection happen?

光从折射率大的介质射向折射率小的介质，且入射角大于临界角 arcsin(n₂/n₁) 时，没有折射光，全部反射。When light goes from a higher to a lower refractive index and the angle of incidence is greater than the critical angle arcsin(n₂/n₁), there is no refracted ray and all of it reflects.

常见折射率是多少？What are typical refractive indices?

空气约 1.000，水 1.333，冰 1.31，普通玻璃约 1.5，钻石 2.417。实际值随波长和温度略有变化。Air about 1.000, water 1.333, ice 1.31, ordinary glass about 1.5 and diamond 2.417. Real values vary slightly with wavelength and temperature.

能举个计算实例吗？Can you show a worked example?

例如在「折射角计算器（斯涅尔定律，含常见介质）」中填 入射介质 = 空气，折射介质 = 水，入射角（与法线夹角，度） = 30，结果区显示：n₁ → n₂：1 → 1.333；折射角 θ₂：22.0301°；偏折角：7.9699°；光线：偏向法线（进入光密介质）；临界角：无（n₁ ≤ n₂ 不会全反射）For example, entering First medium = Air (1.000), Second medium = Water (1.333), Angle of incidence (from normal, degrees) = 30 in the Angle of Refraction Calculator (Law of Refraction, Common Media) gives: n₁ → n₂: 1 → 1.333; Angle of refraction θ₂: 22.0301°; Deviation: 7.9699°; Ray: Bends towards the normal (into a denser medium); Critical angle: None (no total internal reflection when n₁ ≤ n₂)

哪些输入会被检查？Which inputs are validated?

「折射角计算器（斯涅尔定律，含常见介质）」会检查这些输入——「自定义 n₁」、「自定义 n₂」：可留空；「入射角（与法线夹角，度）」：所选方式用到时必须填写；绝对值超过 10¹⁵ 的数也会被拒绝。不符合时结果区显示具体提示，不会给出数字。The Angle of Refraction Calculator (Law of Refraction, Common Media) checks its inputs — "Custom n₁", "Custom n₂": optional; "Angle of incidence (from normal, degrees)": required when the chosen option uses it; numbers above 10¹⁵ in absolute value are rejected too. When a value fails, the result area names the problem instead of showing a number.

有哪些选项可以调整？What options can I adjust?

「折射角计算器（斯涅尔定律，含常见介质）」的设置：「入射介质」可选 空气、水、玻璃、冰、钻石、自定义（默认 空气）；「自定义 n₁」默认 1；「折射介质」可选 空气、水、玻璃、冰、钻石、自定义（默认 水）；「自定义 n₂」默认 1.5；「入射角（与法线夹角，度）」默认 30。每次生成结果都按当前设置处理。Settings in the Angle of Refraction Calculator (Law of Refraction, Common Media) — "First medium": Air (1.000), Water (1.333), Glass (1.5), Ice (1.31), Diamond (2.417), Custom (default Air (1.000)); "Custom n₁" default 1; "Second medium": Air (1.000), Water (1.333), Glass (1.5), Ice (1.31), Diamond (2.417), Custom (default Water (1.333)); "Custom n₂" default 1.5; "Angle of incidence (from normal, degrees)" default 30. The result always uses the current settings.

计算结果可以用于作业或工程吗？Can I use the results for homework or engineering?

「折射角计算器（斯涅尔定律，含常见介质）」使用教科书标准公式（公式写在说明和常见问题中），适合学习和估算核对；涉及安全的工程设计请以规范和实测为准。The Angle of Refraction Calculator (Law of Refraction, Common Media) uses standard textbook formulas (given in the description and FAQ), which is good for learning and checking estimates; for safety-critical engineering follow codes and measured values.

「折射角计算器（斯涅尔定律，含常见介质）」免费吗？需要注册吗？Is the Angle of Refraction Calculator (Law of Refraction, Common Media) free? Do I need an account?

「折射角计算器（斯涅尔定律，含常见介质）」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Angle of Refraction Calculator (Law of Refraction, Common Media) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.