Total internal reflection happens when light traveling in a more optically dense medium, such as glass or water, reaches a boundary with a less optically dense medium, such as air, at a large enough angle. Instead of refracting out, the light reflects completely back into the dense medium. This effect is important because it lets light be guided with very little loss.
It explains how optical fibers carry signals and how prisms redirect light in binoculars, cameras, and scientific instruments.
The key idea is that refraction bends light away from the normal when it enters a medium with a lower refractive index. As the angle of incidence increases, the refracted ray bends closer to the boundary until it reaches 90 degrees at the critical angle. For angles greater than the critical angle, no refracted ray can pass into the second medium, so all the light reflects internally.
The critical angle depends on the refractive indices of the two materials and is found using Snell's law.
Understanding Physics: Total Internal Reflection
Optical density in this topic does not mean ordinary mass density. It describes how strongly a material slows light. Light has the same frequency on both sides of a boundary, but its speed and wavelength change.
At the boundary, the incoming light wave makes electric fields in both materials oscillate. Usually, these oscillations produce a wave that carries energy across the boundary. Beyond the limiting angle, a small field still extends into the less optically dense material, but it fades away within a very short distance.
It does not carry energy off as a travelling beam. The energy remains in the original material and forms the reflected beam.
Angles cause many mistakes in this subject. Every angle used in the rule is measured from the normal, which is an imaginary line at right angles to the surface. It is not measured from the surface itself.
A ray that looks nearly parallel to a flat boundary therefore has a large angle of incidence. The critical angle changes with colour because refractive index changes slightly with wavelength. Blue light is usually slowed more than red light in glass.
This means the limiting angle is not exactly identical for every colour. In precision optical equipment, this can affect image quality and the path taken by different colours.
An optical fibre has a central core surrounded by cladding with a slightly lower refractive index. Light entering at a suitable direction stays mainly in the core because it repeatedly meets the core and cladding boundary under the required conditions. The fibre cannot accept light from every direction.
Its acceptance angle determines how carefully a source must be aligned. Sharp bends can cause light to meet the boundary at too small an angle, allowing some energy to escape.
Real fibres therefore lose some signal through bending, tiny defects, absorption, and scattering, even though reflection at an ideal boundary is extremely efficient. This matters in internet cables, medical endoscopes, and sensors.
Total internal reflection can be used to detect contact with a surface. A prism can reflect light internally while its face touches air. If water, oil, or a fingertip touches that face, the outside refractive index changes.
Some light can then pass out instead of reflecting, so a detector sees less reflected light. Touch screens and some fingerprint readers use versions of this idea. In a school practical, a semicircular acrylic block helps because a ray can enter the curved face nearly along a radius, avoiding bending at that first surface.
Use a dim room, trace the rays carefully, and mark the normal before measuring. Laser beams must never be aimed at eyes or shiny surfaces.
Key Facts
- Total internal reflection occurs only when light travels from higher refractive index to lower refractive index.
- Snell's law: n1 sin θ1 = n2 sin θ2.
- Critical angle formula: sin θc = n2 / n1, where n1 > n2.
- At the critical angle, the refracted ray travels along the boundary, so θ2 = 90°.
- For θ1 > θc, all incident light is reflected back into the original medium.
- For glass to air with n1 = 1.50 and n2 = 1.00, θc = sin^-1(1.00 / 1.50) = 41.8°.
Vocabulary
- Total internal reflection
- The complete reflection of light back into a denser medium when it strikes a boundary at an angle greater than the critical angle.
- Critical angle
- The angle of incidence in the denser medium that makes the refracted ray travel along the boundary at 90 degrees to the normal.
- Refractive index
- A number that describes how much a material slows and bends light compared with a vacuum.
- Normal
- An imaginary line drawn perpendicular to a surface at the point where a light ray strikes it.
- Optical fiber
- A thin transparent strand that guides light by repeated total internal reflection inside its core.
Common Mistakes to Avoid
- Using the angle from the surface instead of the normal is wrong because Snell's law and the critical angle use angles measured from the normal.
- Applying total internal reflection when light goes from air into glass is wrong because total internal reflection requires light to travel from higher refractive index to lower refractive index.
- Forgetting that the critical angle is the boundary case is wrong because total internal reflection occurs only for angles greater than the critical angle, not less than it.
- Assuming some refracted ray still leaves the medium after total internal reflection is wrong because beyond the critical angle the transmitted refracted ray does not propagate into the second medium.
Practice Questions
- 1 Light travels from water with n = 1.33 into air with n = 1.00. Calculate the critical angle for the water to air boundary.
- 2 A ray in glass with n = 1.50 strikes a glass to air boundary at an angle of incidence of 50.0°. The critical angle is 41.8°. Will the ray refract into the air or undergo total internal reflection?
- 3 Explain why optical fibers are designed with a higher refractive index core surrounded by a lower refractive index cladding.