What is the critical angle in light reflection and refraction?

The critical angle in light reflection and refraction is the angle of incidence that produces an angle of refraction of 90 degrees.

In the study of optics, the critical angle is a key concept related to the phenomena of light reflection and refraction. When light travels from a medium with a higher refractive index to one with a lower refractive index, it bends away from the normal. As the angle of incidence increases, so does the angle of refraction, until a point is reached where the refracted light ray runs along the boundary of the two media. This angle of incidence is known as the critical angle.

If the angle of incidence is greater than the critical angle, the light does not pass into the second medium at all. Instead, it is totally internally reflected back into the first medium. This phenomenon is known as total internal reflection. It is the principle behind fibre optics and the mirage effect.

The critical angle can be calculated using Snell's law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the velocities of light in the two media, or equivalently, to the inverse ratio of the refractive indices. When the angle of refraction is 90 degrees, the sine of the angle of refraction is 1, so the critical angle is the inverse sine of the ratio of the refractive indices.

Understanding the critical angle and its implications is crucial in many areas of physics and engineering, including the design of lenses and optical fibres, and the analysis of optical systems.