💡 斯涅尔定律计算器（折射角、折射率、临界角）Snell's Law Calculator (Refraction Angle, Index, Critical Angle)

使用说明与常见问题How-to & FAQ

「斯涅尔定律计算器（折射角、折射率、临界角）」是什么？What is the Snell's Law Calculator (Refraction Angle, Index, Critical Angle) tool?

按 n₁ sin θ₁ = n₂ sin θ₂ 求折射角、入射角或任一侧的折射率；光从高折射率进入低折射率时给出临界角，并判断是否发生全反射。角度从法线量起。本地处理。Solve n₁ sin θ₁ = n₂ sin θ₂ for the refraction angle, the incidence angle or either refractive index. Going from a higher to a lower index it also gives the critical angle and flags total internal reflection. Angles are measured from the normal. Processed locally.

如何使用「斯涅尔定律计算器（折射角、折射率、临界角）」？How do I use the Snell's Law Calculator (Refraction Angle, Index, Critical Angle) tool?

在「斯涅尔定律计算器（折射角、折射率、临界角）」中，填写「求」、「介质 1 折射率 n₁（空气≈1.0003，水 1.333，玻璃≈1.5）」、「入射角 θ₁（度）」、「介质 2 折射率 n₂」、「折射角 θ₂（度）」等参数，结果会随输入实时计算并显示在下方。In the Snell's Law Calculator (Refraction Angle, Index, Critical Angle): Fill in "Solve for", "Index n₁ of medium 1 (air ≈1.0003, water 1.333, glass ≈1.5)", "Incidence angle θ₁ (degrees)", "Index n₂ of medium 2", "Refraction angle θ₂ (degrees)"; results are recalculated instantly as you type.

角度从哪里量？Where are the angles measured from?

从法线（垂直于界面的线）量起，不是从界面量起。光垂直射入时角度是 0°。角度用度，范围 0° 到 90°。From the normal, the line at right angles to the surface, not from the surface itself. Light hitting the surface head-on has an angle of 0°. Angles are in degrees, from 0° to 90°.

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

光从折射率高的介质进入折射率低的介质（如从水到空气），且入射角大于临界角 θc = arcsin(n₂/n₁) 时，没有折射光，全部反射回去。水到空气的临界角约 48.6°。When light goes from a higher-index medium into a lower-index one (water to air, say) at an incidence angle above the critical angle θc = arcsin(n₂/n₁), nothing is refracted and all the light reflects back. Water to air has a critical angle of about 48.6°.

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

真空 1，空气约 1.0003，水 1.333，普通玻璃约 1.5，钻石约 2.42（可见光、室温下的典型值，随波长略有变化）。Vacuum 1, air about 1.0003, water 1.333, ordinary glass about 1.5 and diamond about 2.42 (typical values for visible light at room temperature; they vary slightly with wavelength).

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

例如在「斯涅尔定律计算器（折射角、折射率、临界角）」中填 求 = 折射角 θ₂，介质 1 折射率 n₁（空气≈1.0003，水 1.333，玻璃≈1.5） = 1，入射角 θ₁（度） = 30，介质 2 折射率 n₂ = 1.5，结果区显示：折射角 θ₂：19.4712°；临界角：无：光从低折射率进入高折射率时不会全反射；ℹ n₁ sin θ₁ = n₂ sin θ₂，角度从法线量起For example, entering Solve for = Refraction angle θ₂, Index n₁ of medium 1 (air ≈1.0003, water 1.333, glass ≈1.5) = 1, Incidence angle θ₁ (degrees) = 30, Index n₂ of medium 2 = 1.5 in the Snell's Law Calculator (Refraction Angle, Index, Critical Angle) gives: Refraction angle θ₂: 19.4712°; Critical angle: none: going into a higher index there is no total internal reflection; ℹ n₁ sin θ₁ = n₂ sin θ₂, angles from the normal

哪些输入会被检查？Which inputs are validated?

「斯涅尔定律计算器（折射角、折射率、临界角）」会检查这些输入——「介质 1 折射率 n₁（空气≈1.0003，水 1.333，玻璃≈1.5）」、「入射角 θ₁（度）」、「介质 2 折射率 n₂」、「折射角 θ₂（度）」：可留空；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 Snell's Law Calculator (Refraction Angle, Index, Critical Angle) checks its inputs — "Index n₁ of medium 1 (air ≈1.0003, water 1.333, glass ≈1.5)", "Incidence angle θ₁ (degrees)", "Index n₂ of medium 2", "Refraction angle θ₂ (degrees)": optional; 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?

「斯涅尔定律计算器（折射角、折射率、临界角）」的设置：「求」可选 折射角 θ₂、入射角 θ₁、折射率 n₂、折射率 n₁（默认 折射角 θ₂）；「介质 1 折射率 n₁（空气≈1.0003，水 1.333，玻璃≈1.5）」默认 1；「入射角 θ₁（度）」默认 30；「介质 2 折射率 n₂」默认 1.333；「折射角 θ₂（度）」默认 22。每次生成结果都按当前设置处理。Settings in the Snell's Law Calculator (Refraction Angle, Index, Critical Angle) — "Solve for": Refraction angle θ₂, Incidence angle θ₁, Index n₂, Index n₁ (default Refraction angle θ₂); "Index n₁ of medium 1 (air ≈1.0003, water 1.333, glass ≈1.5)" default 1; "Incidence angle θ₁ (degrees)" default 30; "Index n₂ of medium 2" default 1.333; "Refraction angle θ₂ (degrees)" default 22. 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?

「斯涅尔定律计算器（折射角、折射率、临界角）」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 Snell's Law Calculator (Refraction Angle, Index, Critical Angle) 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.

「斯涅尔定律计算器（折射角、折射率、临界角）」免费吗？需要注册吗？Is the Snell's Law Calculator (Refraction Angle, Index, Critical Angle) free? Do I need an account?

「斯涅尔定律计算器（折射角、折射率、临界角）」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 Snell's Law Calculator (Refraction Angle, Index, Critical Angle) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.