Total internal reflection and Snell's law
Total internal reflection and Snell's law are characteristics frequently used in photonics packaging. Understanding these concepts can help implement effective photonics packaging.
Total internal reflection is a phenomenon that occurs when light travels from a medium with a high refractive index (e.g., water) to a medium with a lower refractive index (e.g., air). If the angle of incidence of the light is greater than a certain critical angle, all of the light is reflected into the medium with the higher refractive index. The following conditions are required for internal reflection to occur.
The refractive indices of the two media through which light passes must be different, and n1 must be greater than n2 (n1 > n2), where n1 is the refractive index of the denser medium and n2 is the refractive index of the less dense medium. The angle of incidence, θ1, must be greater than the critical angle, θc.
This phenomenon of internal reflection can be expressed by a simple formula known as Snell's law, which represents the following relationship.
n1 * sinθ1 = n2 * sinθ2
n1 and n2 represent the refractive indices of the two media, respectively. θ1 is the angle of incidence of light in medium 1, and θ2 is the angle of refraction as light passes into medium 2. Both the angle of incidence and the angle of refraction are measured relative to the normal interface between medium 1 and medium 2.
Therefore, the critical angle for internal reflection can be easily calculated using the relationship from Snell's law. At the moment of total internal reflection, the angle of refraction θ₂ becomes 90°, which means sinθ₂ = 1. Substituting this into Snell's law gives the following.
n₁sinθ₁ = n₂ * 1
sinθ₁ = n₂ / n₁
Here, θ₁ is the critical angle (θc), so the critical angle is as follows.
sinθc = n2 / n1
θc = sin⁻¹(n2/n1)
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