Understanding Total Internal Reflection

Total Internal Reflection

• When light moves from one medium to another, some is reflected and some is refracted.
• Light slows down moving from air into acrylic or water, bending it toward the normal.
• Light speeds up moving between mediums like acrylic into air, bending it away from the normal.
• In this situation, the angle of refraction is greater than the angle of incidence
• As the angle of incidence increases, the angle of refraction also increases.
• Eventually, the angle of refraction will become 90°.
• Critical angle: The angle of incidence producing a refracted angle of 90°.
• If the angle of incidence increases beyond the critical angle, the refracted ray won't exit the medium but reflect back into it.
• Total internal reflection: When the angle of incidence is greater than the critical angle, resulting in the refracted ray disappearing and only a reflected ray being seen.
• Total internal reflection happens:
• Light moves slower in the first medium than in the second.
• The angle of incidence is large enough that no refraction occurs in the second medium, so the ray reflects back into the first.
• Water's critical angle is 48.8°, and angles of incidence greater than 48.8° cause total internal reflection in water.
• The critical angle is a physical property of a medium.

Diamonds

• Diamond's sparkle comes from the cut of the diamond faces, combined with its high index of refraction (n = 2.42).
• Diamond's high refractive index results in a small critical angle of 24.4°.
• A lot of the light hitting a diamond undergoes total internal reflection.
• Light can bounce inside a diamond several times before exiting through a top face, causing the appealing "sparkling" effect.

Fibre Optics

• Fibre optics transmit information along a glass cable using light.
• Cables have a small critical angle so entering light will have an incidence angle greater than it.
• High-purity glass and special plastics (like Lucite) have small critical angles.
• Fibre optics are used for phones, computers, TVs, movies and cars
• Endoscope: A fibre-optic device in medicine which lets doctors check the health of internal organs.
• It uses two fibre-optic bundles: one shines light into the body, the second carries the reflected light back to the instrument.

Triangular Prism

• Triangular prisms exhibit total internal reflection.
• Glass's critical angle is about 41.1°; total internal reflection happens if a prism is oriented so that its angle of incidence exceeds 41.1°.
• Prisms are better at reflecting light than mirrors because the prism reflects nearly 100% of the light internally.
• The emergent ray can be either 90° or 180° relative to the incident ray, depending on how the prism is placed.

Retro-reflectors

• Retro-reflector: An optical device returning any incident light back in exactly the same direction from which it came.
• Prism orientation is an example of a retro-reflector because the emergent ray is parallel to the incident ray as a result of two total internal reflections.
• Corner cube retro-reflector: Cutting off the corner of a glass cube produces this, with three perpendicular faces reflecting an incident ray coming from any direction back.
• The Apollo 11 astronauts left a Laser Ranging Retro-Reflector (LR³) on the Moon.
• The LR³ used 100 corner cube retro-reflectors in a 10 × 10 grid.
• Scientists on Earth used the device to shine a laser beam at the Moon and bounce it off the LR³, and determine the Earth–Moon distance with an accuracy of 3 cm.
• Bike reflectors, reflective strips on clothing and helmets, and road signs use tiny retro-reflectors in the paint.