This animation illustrates Snell’s law of refraction at a curved interface between two optical media. An interactively positionable light ray strikes the surface and is both reflected and refracted, depending on the adjustable refractive index of the second medium. The angular relationships between the incident, reflected, and refracted rays are visualized through dynamic angle markers.
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Animation Description
The animation shows a light ray emitted from a flashlight striking a curved interface between air (refractive index \( n_1 = 1 \)) and an optically denser medium. At the point of incidence, the ray is partially reflected and partially refracted into the second medium.
The refraction follows Snell’s law:
\[ n_1 \sin \alpha = n_2 \sin \beta \]
Here, \( \alpha \) is the angle of incidence and \( \beta \) is the angle of refraction, each measured from the surface normal. For reflection, the law of reflection applies: the angle of incidence \( \alpha \) equals the angle of reflection \( \alpha’ \).
The interface is represented by a cubic curve whose shape can be modified using two control points (green circles). At each point on the curve, the local normal is calculated to determine the correct angles for reflection and refraction. When the angle of incidence is sufficiently large and light travels from an optically denser to an optically less dense medium, total internal reflection can occur – the refracted ray then disappears.
Interactive Controls
The animation offers extensive interaction options:
- Refractive index n₂: Adjustable from 1.0 to 10.0. Higher values result in stronger refraction toward the normal.
- Flashlight: Can be freely positioned. The light ray automatically aligns toward the target position.
- Ray direction: The red endpoint of the light ray can be dragged to change the angle of incidence.
- Control points: The two green circles allow deformation of the interface – from concave through flat to convex.
The animation displays in real time the angle of incidence \( \alpha \), the angle of reflection \( \alpha’ \), and the angle of refraction \( \beta \) using labeled angle arcs. The yellow circle marks the point of incidence on the interface, and the dashed line indicates the surface normal.
Physical Background
Light refraction occurs due to the different propagation speeds of light in different media. The refractive index \( n \) represents the ratio of the speed of light in a vacuum to the speed of light in the medium. When light travels from an optically less dense to an optically denser medium (e.g., from air into glass), the light ray bends toward the normal – the angle of refraction is smaller than the angle of incidence.
Overview
| Title | Light Refraction at Curved Interfaces |
| Target Audience | Teachers and Lecturers |
| License | Open Source – CC BY 4.0 |
| Attribution Notice | Created with AI assistance |