Total internal reflection

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Total internal reflection is an optical phenomenon that happens when a ray of light strikes a medium boundary at an angle larger than a particular critical angle with respect to the normal to the surface. If the refractive index is lower on the other side of the boundary, no light can pass through and all of the light is reflected. The critical angle is the angle of incidence above which the total internal reflection occurs.

When light crosses a boundary between materials with different refractive indices, the light beam will be partially refracted at the boundary surface, and partially reflected. However, if the angle of incidence is greater (i.e. the ray is closer to being parallel to the boundary) than the critical angle – the angle of incidence at which light is refracted such that it travels along the boundary – then the light will stop crossing the boundary altogether and instead be totally reflected back internally. This can only occur where light travels from a medium with a higher [n1=higher refractive index] to one with a lower refractive index [n2=lower refractive index]. For example, it will occur when passing from glass to air, but not when passing from air to glass.


Optical description

Total internal reflections can be demonstrated using a semi-circular glass block. A "ray box" shines a narrow beam of light (a "ray") onto the glass. The semi-circular shape ensures that a ray pointing towards the centre of the flat face will hit the curved surface at a right angle; this will prevent refraction at the air/glass boundary of the curved surface. At the glass/air boundary of the flat surface, what happens will depend on the angle. Where θc is the critical angle measurement which is caused by the sun or a light source (measured normal to the surface):

  • If θ < θc, the ray will split. Some of the ray will reflect off the boundary, and some will refract as it passes through.
  • If θ > θc, the entire ray reflects from the boundary. None passes through. This is called total internal reflection.

This physical property makes optical fibers useful and prismatic binoculars possible. It is also what gives diamonds their distinctive sparkle, as diamond has an extremely high refractive index.

Critical angle

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