Applications of Total Internal Reflection

From Physics to Practical Devices

Total internal reflection is not just a laboratory curiosity. The fact that light can be completely trapped inside a denser medium, with zero loss at each bounce, makes it one of the most useful phenomena in optics. Two important applications stand out: reflecting prisms that bend or flip light beams with perfect efficiency, and optical fibres that carry light signals over hundreds of kilometres. Both rely on the same underlying principle you studied in the previous topic.

Bending Light with Prisms: The Reflecting Prism

How a Simple Glass Prism Replaces a Mirror

Mirrors reflect light, but they never do it perfectly. Even the best silvered mirror absorbs a tiny fraction of the light, and the reflected image is slightly dimmer than the incoming beam. A reflecting prism (a prism specifically designed to exploit total internal reflection) sidesteps this problem entirely. Because total internal reflection bounces back every bit of light with no transmission loss, a prism reflection is brighter and cleaner than a mirror reflection.

The prism used most often for this purpose has a right-angled triangular cross-section, with angles of $45°$, $45°$, and $90°$. This is called a $45°$-$45°$-$90°$ prism.

Turning a Beam by $90°$

Fig 9.13(a): A $45°$-$45°$-$90°$ prism bending a ray by $90°$ through total internal reflection at the hypotenuse

Picture a ray of light entering one of the two shorter faces of the prism straight on (perpendicular to the surface, so it passes through without bending). It then hits the hypotenuse (the longest face) from inside the glass. The angle of incidence at this surface is $45°$.

Now, for total internal reflection to kick in, the critical angle of the glass must be less than $45°$. Looking at the values from the previous topic, crown glass has a critical angle of about $41°$ and dense flint glass about $37°$, both comfortably below $45°$. So the $45°$ incidence angle exceeds the critical angle, and the light undergoes total internal reflection. It bounces off the hypotenuse and exits through the second short face, having turned through a right angle.

Turning a Beam by $180°$

Fig 9.13(b): The same type of prism arranged to send a ray back in the opposite direction, a $180°$ turn

The same $45°$-$45°$-$90°$ prism can also send light straight back the way it came. By changing how the prism is oriented relative to the incoming beam, the light enters one short face, totally reflects off the hypotenuse, and leaves through the other short face heading in the reverse direction. The beam has effectively been folded back on itself.

Inverting an Image Without Changing Its Size

Fig 9.13(c): A pair of reflecting prisms inverting an image without any change in size

A particularly clever arrangement uses two reflecting prisms together. Light from an upright object enters the first prism, bounces off its hypotenuse by total internal reflection, then passes into the second prism, where it bounces again. The combined effect of these two reflections flips the image upside down, but the image stays the same size as the original. This principle is used in devices like binoculars and periscopes.

Why the Critical Angle Must Be Below $45°$

The whole scheme depends on one geometric fact: the light strikes the hypotenuse at exactly $45°$. If the critical angle of the prism material were $45°$ or higher, the light would partly refract through the hypotenuse instead of reflecting completely. Crown glass ($i_c \approx 41°$) and dense flint glass ($i_c \approx 37°$) both satisfy this condition, which is why they are the standard choices for reflecting prisms.

Guiding Light Over Long Distances: Optical Fibres

The Problem Optical Fibres Solve

Imagine you need to send a signal, say a phone call or a video stream, from one city to another. Electrical cables work, but they suffer from signal loss and interference over long distances. Light, if you could somehow guide it along a flexible path without losing it, would be far more efficient. That is exactly what an optical fibre does. It acts as a pipe for light, trapping the signal inside through repeated total internal reflections and carrying it across kilometres with remarkably little loss.

What an Optical Fibre Looks Like Inside

An optical fibre is a very thin, flexible strand made of high-quality composite glass or quartz. It has two distinct layers:

• Core — the central part through which the light actually travels. It has a higher refractive index.
• Cladding — the outer layer that surrounds the core. It has a lower refractive index than the core.

This difference in refractive index is the key to everything. Because the core is optically denser than the cladding, light hitting the core-cladding boundary from inside the core can undergo total internal reflection, provided it strikes at an angle greater than the critical angle.

How Light Stays Trapped

Fig 9.14: Light bouncing along an optical fibre by repeated total internal reflection

When a light signal enters one end of the fibre at a suitable angle, it hits the core-cladding boundary and totally reflects back into the core. The reflected ray then crosses the core and hits the opposite wall, again at an angle exceeding the critical angle, so it reflects once more. This zigzag pattern continues along the entire length of the fibre.

The fibre is engineered so that light reflected from one side of the core always strikes the other side at an angle larger than the critical angle. This ensures that total internal reflection occurs at every single bounce, and no light leaks out through the cladding. Since total internal reflection involves zero intensity loss (all the light comes back), the signal stays strong over long distances.

A remarkable property of optical fibres is that they work even when bent into a curve. The internal angles adjust as the fibre curves, but as long as the light continues to hit the walls beyond the critical angle, total internal reflection persists. This flexibility is what earns the optical fibre its nickname: an optical pipe.

What Optical Fibres Are Used For

Bundles of optical fibres serve a wide range of purposes:

• Telecommunications — Audio and video signals are converted into light by devices called transducers (devices that convert one form of energy to another). The light pulses travel through the fibre, and at the receiving end, another transducer converts them back into electrical signals. This is the backbone of modern internet and telephone networks.
• Medical endoscopy — A fibre bundle can be inserted into the body to allow doctors to visually examine internal organs such as the oesophagus (food pipe), stomach, and intestines without surgery. The fibres carry light in and an image back out, functioning as a light pipe.
• Decorative lighting — You may have seen lamps with a fountain of thin plastic fibres, each glowing at its tip. The base contains an electric bulb, and light travels through each fibre by total internal reflection, emerging as a bright dot at the free end.
• Optical signal transmission — Beyond electrical-to-light conversion, fibres can also carry purely optical signals directly, useful in scientific instruments and industrial sensing.

Why Purity Matters

Total internal reflection prevents light from escaping sideways, but the glass material itself can absorb some light as the signal passes through. The main requirement for practical optical fibres is that this absorption must be extremely small. Achieving this requires glass of extraordinary purity.

Through careful purification and specialised manufacturing processes, modern silica glass fibres can transmit more than 95% of the light over a fibre length of 1 km. To appreciate how remarkable this is, consider that a block of ordinary window glass just 1 km thick would absorb virtually all the light passing through it. The difference comes down to the removal of trace impurities that would otherwise scatter or absorb the photons during their journey.