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.
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.