The angle of incidence at which light travels fastest is when it passes from one medium to another with a higher refractive index, and the angle is exactly 0 degrees. This situation is known as "normal incidence."
When light travels from one medium to another, it can change direction due to a property called refraction. Refraction occurs because light travels at different speeds in different materials. The speed of light in a vacuum is constant, but when it enters a different medium (such as glass or water), its speed changes, and it bends as a result.
The refractive index (n) of a medium is a measure of how much the speed of light is reduced in that medium compared to its speed in a vacuum. The formula for calculating the angle of refraction (θ) as light passes from one medium to another is given by Snell's Law:
n1 * sin(θ1) = n2 * sin(θ2)
where: n1 = refractive index of the first medium (incident medium) θ1 = angle of incidence (measured from the normal) n2 = refractive index of the second medium (refracted medium) θ2 = angle of refraction (measured from the normal)
When light passes from a medium with a lower refractive index (n1) to a medium with a higher refractive index (n2), such as from air (n1 ≈ 1) to glass (n2 ≈ 1.5), there is a critical angle of incidence, known as the "critical angle." At this angle of incidence, the angle of refraction (θ2) becomes 90 degrees, meaning the light ray travels along the boundary between the two media. Beyond the critical angle, the light undergoes total internal reflection and doesn't pass through to the other side.
However, when light travels from a medium with a higher refractive index to one with a lower refractive index (e.g., from glass to air), there is no critical angle, and the light doesn't undergo total internal reflection. In this case, the angle of incidence is 0 degrees (normal incidence), and the light travels fastest in the second medium (air) since it is returning to its higher speed in a vacuum.
The speed of light in a medium is related to the refractive index by the equation:
v = c / n
where: v = speed of light in the medium c = speed of light in a vacuum (approximately 299,792 kilometers per second)
As the refractive index (n) increases, the speed of light (v) in the medium decreases. So, when light passes from a medium with a higher refractive index to one with a lower refractive index, it returns to its higher speed in a vacuum, and this happens at normal incidence (0 degrees angle of incidence).