Prism Refraction Simulator

Glass 種類

屈折率 n

プリズム頂角 A

入射角 θ₁

Spectrum分散表示法線Vector表示

Results

屈折角 θ₂

—

偏角 δ

—

臨界角

—

最小偏角 δmin

—

Prism

Theory & Key Formulas

$n_1\sin\theta_1 = n_2\sin\theta_2$
偏角：$\delta = \theta_1 + \theta_4 - A$
臨界角：$\theta_c = \arcsin(1/n)$
最小偏角：$\delta_{min} = 2\arcsin(n\sin\frac{A}{2}) - A$

FAQ

What is Snell's law?

The law governing light bending at medium boundaries: n₁sinθ₁=n₂sinθ₂. Light bends toward the normal when entering a denser medium.

Why does a prism create a rainbow?

Glass refractive index varies with wavelength (dispersion). Red (long wavelength) has lower n, blue (short) has higher n, so they bend at different angles.

What is total internal reflection?

When light travels from dense to less dense medium, angles exceeding the critical angle result in 100% reflection. Basis of optical fiber and endoscopes.

What is minimum deviation angle?

At a specific incidence angle, the deviation angle is minimized. At this point, light travels parallel to the base inside the prism.

🙋

I can see the simulation updating, but what exactly is being calculated here?

🎓

Great question! The simulator solves the governing equations in real time as you move the sliders. Each parameter you control directly affects the physical outcome you see in the graph. The key is to build an intuitive feel for how each variable influences the result — that's how engineers develop physical judgment.

🙋

So when I increase this parameter, the curve shifts significantly. Is that a linear relationship?

🎓

It depends on the model. Some relationships are linear, but many engineering phenomena are nonlinear. Try moving the sliders to extreme values and see if the output changes proportionally — if the graph shape changes, that's a sign of nonlinearity. This hands-on exploration is exactly what simulations are best for.

🙋

Where is this kind of analysis actually used in practice?

🎓

Constantly! Engineers run these calculations during the design phase to quickly screen parameters before investing in expensive physical tests or detailed finite element simulations. Getting comfortable with these simplified models is a real engineering skill.

補足情報

📊 代表的なGlass 分散特性（ナトリウムD線 λ=589nm 基準）

材質	屈折率 n_D	アッベ数 V	用途
冕Glass (Crown)	1.52	64	レンズ前群・眼鏡
フリントGlass (Flint)	1.62	36	色収差補正・後群
BK7光学Glass	1.517	64.2	精密光学機器標準
重フリントGlass (SF)	1.75	28	ペリスコープ・特殊用途
溶融石英 (SiO₂)	1.458	68	UV光学・光ファイBar
水 (20°C)	1.333	56	自然界・水中光学
ダイヤモンド	2.417	55	宝石・高圧光学窓

※ アッベ数 V=(n_D−1)/(n_F−n_C)。Vが大きいほど分散が小さい（色収差が少ない）。

What is Prism Refraction Simulator?

Prism Refraction Simulator is a fundamental topic in engineering and applied physics. This interactive simulator lets you explore the key behaviors and relationships by directly manipulating parameters and observing real-time results.

By combining numerical computation with visual feedback, the simulator bridges the gap between abstract theory and physical intuition — making it an effective learning tool for students and a rapid-verification tool for practicing engineers.

Physical Model & Key Equations

The simulator is based on the governing equations of Prism Refraction Simulator. Understanding these equations is key to interpreting the results correctly.

Each parameter in the equations corresponds to a slider in the control panel. Moving a slider changes the equation's solution in real time, helping you build a direct connection between mathematical expressions and physical behavior.

Real-World Applications

Engineering Design: The concepts behind Prism Refraction Simulator are applied across mechanical, structural, electrical, and fluid engineering disciplines. This tool provides a quick way to estimate design parameters and sensitivity before committing to full CAE analysis.

Education & Research: Widely used in engineering curricula to connect theory with numerical computation. Also serves as a first-pass validation tool in research settings.

CAE Workflow Integration: Before running finite element (FEM) or computational fluid dynamics (CFD) simulations, engineers use simplified models like this to establish physical scale, identify dominant parameters, and define realistic boundary conditions.

Common Misconceptions and Points of Caution

Model assumptions: The mathematical model used here relies on simplifying assumptions such as linearity, homogeneity, and isotropy. Always verify that your real system satisfies these assumptions before applying results directly to design decisions.

Units and scale: Many calculation errors arise from unit conversion mistakes or order-of-magnitude errors. Pay close attention to the units shown next to each parameter input.

Validating results: Always sanity-check simulator output against physical intuition or hand calculations. If a result seems unexpected, review your input parameters or verify with an independent method.