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Total internal reflection of light

When light passes from a medium with a higher refractive index into a medium with a lower refractive index (for example, from glass into air), refracted light only occurs when the angle of incidence θ is less than a certain critical value. If θ1 exceeds this critical angle, the value of sin θ2 in the refraction formula (Equation 1.2) must be greater than 1, a condition that cannot be satisfied by the real number θ2. In this case, no refracted light occurs, and all the incident light energy appears in the reflected light. This condition is called total internal reflection. For example, for glass with a refractive index of 1.5, the critical angle for total internal reflection at the glass-air interface can be calculated using the refraction formula, where n1 = 1.5, n2 = 1, and sin0 = 1, yielding a critical angle θ1 = 41°49'.

Total internal reflection can be used to create reflective surfaces without loss of light. This technique is used in prismatic binoculars, reflective signage, and certain lighting fixtures. It can also be used in fiber optics. In fiber optics, light travels along a glass rod or fiber, where the path of light can be curved.

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