The interactive animation shows how a light beam is reflected and refracted on a semi-transparent surface (Snell’s law of refraction).
Instructions for Use
As with all animations, the windows can be enlarged or reduced by clicking on them.
After starting the application, you can view the animation in full-screen mode. To do this, click on “View” and then on “Full screen”:
To exit full screen mode, press the Esc key.
Description of the Animation
To change the angle of incidence of the light beam, click on the top of the spotlight and move the mouse to the left or right.
Alternatively, you can also change the target point of the light beam.
To do this, move the point at the bottom of the animation.
This animation also allows curved surfaces to be displayed. Change the shape of the surface using the points on the right and left edges of the animation.
The refractive index of the medium can be set between 1 and 10.
The maximum refractive index observed in a naturally occurring material is 2.42 (diamond). Materials produced in laboratories can reach higher refractive indices. Experiments have produced artificial materials with refractive indices of over 4. Such high-performance materials are often developed for specialized applications such as optical lenses, lasers and other optical devices.
Physical Background
Snell’s law of refraction describes how a light beam behaves at the boundary between two media:
\[ n_1 \cdot \sin(\alpha_1) = n_2 \cdot \sin(\alpha_2) \]
- n₁, n₂: Refractive indices of the two media
- α₁: Angle of incidence (measured from the normal to the surface)
- α₂: Angle of refraction
The law of reflection also applies: the angle of incidence equals the angle of reflection.
To view the formulas in the animation, click on the content window of the animation.
Refraction in Everyday Life
Refraction is not just a textbook phenomenon — it shapes what we see every day:
- The bent straw: A drinking straw in a glass of water appears to break at the surface. The light from the submerged part changes direction as it passes from water into air, shifting the apparent position of the straw.
- Pools look shallower than they are: When you look down into a swimming pool, the bottom appears closer than it actually is. Light traveling from the pool floor bends away from the normal as it exits the water, making the depth seem smaller.
- Mirages on hot roads: On a hot day, the air just above the road surface is less dense than the air above it. This gradient in refractive index bends light upward, creating the illusion of a reflective puddle — a mirage (Fata Morgana).
- Eyeglasses and contact lenses: Corrective lenses work by refracting light so that it converges precisely on the retina. The lens curvature and the refractive index of the glass or plastic determine the corrective power.
- Rainbows: Sunlight enters a raindrop, refracts at the surface, reflects inside the drop, and refracts again on the way out. Because the refractive index depends slightly on wavelength (dispersion), white light is separated into its spectral colors.
Total Internal Reflection and Critical Angle
When light travels from an optically denser medium (higher n) into a less dense medium (lower n), the refracted ray bends away from the normal. As the angle of incidence increases, the refraction angle approaches 90°. At a specific angle — the critical angle αc — the refracted ray grazes along the boundary surface. Beyond this angle, no light passes through: all of it is reflected back into the denser medium. This phenomenon is called total internal reflection.
The critical angle can be calculated from Snell’s law by setting α₂ = 90°:
\[ \sin(\alpha_c) = \frac{n_2}{n_1} \]
This only works when n₁ > n₂ (light moving from the denser into the less dense medium).
Applications of total internal reflection:
- Fiber optics: Light signals travel through glass fibers over hundreds of kilometers with minimal loss, because total internal reflection keeps the light trapped inside the fiber core.
- Diamond brilliance: Diamond has a very high refractive index (2.42), resulting in a small critical angle of about 24.4°. Light entering the top of a well-cut diamond undergoes multiple total internal reflections before exiting, creating the characteristic sparkle.
- Endoscopy: Medical endoscopes use bundles of optical fibers to transmit images from inside the body, relying on total internal reflection to guide the light.
Refractive Indices of Common Materials
The following table lists the refractive indices of frequently encountered materials (measured at a wavelength of approximately 589 nm — the sodium D-line). Use these values in the animation to simulate realistic scenarios.
| Material | Refractive Index n |
|---|---|
| Vacuum | 1.00 (exactly) |
| Air (at 20 °C) | 1.000293 |
| Water | 1.33 |
| Ethanol | 1.36 |
| Olive oil | 1.47 |
| Crown glass | 1.52 |
| Flint glass | 1.62 |
| Sapphire | 1.77 |
| Diamond | 2.42 |
Historical Context — Who Was Snellius?
Willebrord Snellius (1580–1626) was a Dutch mathematician and astronomer at the University of Leiden. Around 1621, he discovered the mathematical relationship between the angles of incidence and refraction — though he never published his finding. His result became known through Christiaan Huygens, who referenced Snellius’s unpublished manuscript decades later.
Independently, the French philosopher and mathematician René Descartes (1596–1650) published the same law in his work Dioptrique in 1637 — without crediting Snellius. For this reason, the law is called “Snell’s Law” in the English-speaking world and “Loi de Descartes” in France.
What is less well known: the relationship was already described by the Persian scholar Ibn Sahl as early as 984, more than 600 years before Snellius. Ibn Sahl used the law to design optimal lens shapes — a remarkable achievement of medieval Islamic optics.
Frequently Asked Questions
Does light slow down in glass?
Yes. The speed of light in a medium is c/n, where c is the speed of light in vacuum and n is the refractive index. In glass (n ≈ 1.5), light travels at about two-thirds of its vacuum speed. The frequency remains the same, but the wavelength decreases.
Why does light bend toward the normal when entering a denser medium?
When a wavefront enters a medium where the speed of light is lower, the part of the wavefront that arrives first slows down while the rest continues at the original speed. This causes the wavefront to pivot, changing the direction of propagation — the ray bends toward the normal.
What happens at perpendicular incidence (0°)?
When light hits the surface exactly along the normal (α₁ = 0°), Snell’s law gives sin(0°) = 0 on both sides. The light passes straight through without changing direction — no refraction occurs. However, some of the light is still reflected (partial reflection).
Is the refractive index the same for all colors of light?
No. The refractive index depends slightly on the wavelength (color) of the light — a phenomenon called dispersion. Blue light is refracted more strongly than red light. This is why a prism splits white light into a rainbow of colors, and why chromatic aberration occurs in simple lenses.
Can the refractive index be less than 1?
For visible light in ordinary materials, no — n is always greater than or equal to 1. However, for certain types of radiation (e.g., X-rays) in some materials, the refractive index can be slightly less than 1. In specially engineered metamaterials, even negative refractive indices have been achieved.
Overview and Download
| Title | Snell’s Law of Refraction |
| Target Audience | Teachers and Lecturers |
| Platforms | Microsoft® Windows® Apple® Macintosh® (version-dependent) |
| Features | Full-screen mode Lossless scaling Large screens and projectors supported |
| License | Freeware |
| Download | Contact |
Related Animations
- Snell’s Law – Interactive Web Animation directly in the browser
- All HD animations
- Information for teachers
Didactic Idea
The scene shown can be partially simulated with an experimental setup. The advantage of the animation is that the geometric relationships can be quickly clarified.
Source information
Authoring tool: Adobe Animate (Note: This software can now only be used to a limited extent for modern animations.)