25.4 Total Internal Reflection

The figure shows that if the second medium's index of refraction is less than the first, the ray will not bend.
Imagine what will happen when the incident angle is increased.
The incident angle is that.

When the second medium has an index of refraction less than the first, total internal reflection can occur for any incident angle greater than the critical angle.

As shown in the figure, the above equation was written for a light ray that travels in medium 1 and reflects in medium 2.

The equation can be used to find the critical angle if the second medium has an index of refraction less than the first.

Any light that strikes the plastic at an angle greater than the surface will be reflected.

The inside surface of the clear plastic will be a perfect mirror for such rays without the need for silvering.

Any combination of materials can produce total internal reflection.
The critical angle for a ray going from water to air is the same as the critical angle for a diamond going from diamond to air.
Since the second medium must have a smaller index of refraction, there is no total reflection for rays going in the other direction.

It is used in communications to transmit signals.
It is easy to coat the outside of the fiber with a material that has an appropriate Refractive index in order to get a smaller index of refraction.
The rays reflect around the corners and make the fibers into light pipes.

Light entering a thin fiber may strike the inside surface at large or grazing angles and is completely reflected if these angles exceed the critical angle.

The angles of reflection and incidence remain large, so the rays continue down the fiber.

Light is transmitted down one fiber bundle to illuminate internal parts, and the reflected light is transmitted back out through another to be observed.

arthroscopic surgery on the knee joint can be done using cutting tools attached to the endoscope.
The lassoing of an idiosyncrasy can be used to obtain samples.

Diagnostic and therapeutic uses are plentiful.
The flexibility of the bundle allows it to navigate around difficult and small regions in the body.
A laser beam can be transmitted to burn away plaques in major arteries as well as deliver light which can be used to fight cancer.
Microsurgery and remote surgery can be done using optical fibers because the surgeon's fingers don't need to touch the tissue.

The core of a bundle is surrounded by a material that has a lower index of refraction.

Light could pass between fibers if they were not covered.
Since there is no light entering the core, no light can be transmitted between the fibers.
A quality image is formed at the other end of the fiber due to the fact that most of the light is propagated along the length of the fiber.
The optical fibers are flexible and durable because of the protective layer.

Even when fibers are in contact with one another, the bundle's material has a lower index of refraction than the core to ensure total internal reflection.

The ends of bundles of fibers are being designed with special tiny lens that can be attached to them.

A tiny spot can be imaged when light emerges from a fiber bundle.
Quality images of a region inside the body can be obtained from the spot being scanned.
Special minute optical filters that are inserted at the end of the fiber bundle have the ability to image tens of microns below the surface without cutting the surface--non-intrusive diagnostics.
This can be used to determine the extent of cancer in the stomach and bowel.

Laser signals along optical fibers carry most telephone conversations and Internet communications.

There are optical fiber cables on the ocean floor and underground.
For long distances, optical fiber communication systems offer several advantages over electrical systems.
The fibers can be made so transparent that light can travel many kilometers before it becomes dim.
The low loss is the property of optical fibers.
Lasers emit light with characteristics that allow more conversations in one fiber than with electric signals on a single conductor.
High bandwidth is the property of optical fibers.
The effects of optical signals in other fibers are not as bad as they are in one fiber.
The property of optical fibers is called reduced crosstalk.
The characteristics of laser radiation will be explored in a later chapter.

A light ray that strikes an object consisting of two reflecting surfaces is reflected back to the direction from which it came.

This is true when the reflecting surfaces are not straight.
Corner reflectors on buttons on bicycles, cars, and warning signs return light in the direction from which it originated.
It cost more to place one on the moon.
To measure the gradually increasing distance to the moon, laser signals can be bounced from that corner reflector.

These binoculars have corner reflectors that reflect the light into the observer's eyes.

Diamonds sparkle more than other materials because of their total internal reflection and large index of refraction.

When light enters a diamond, it has trouble getting back out because of the critical angle.

Facets on diamonds are meant to make this unlikely, so that the light can only exit in certain places.
Good diamonds are clear so that the light makes many internal reflections and is concentrated at the few places it can exit.

Those colors are the result of dispersion.
Structural defects of the crystal lattice and the inclusion of minute quantities of graphite and other materials give colored diamonds their color.
Around 50% of the world's clear diamonds come from central and southern Africa, and around 90 percent of the world's pink, red, champagne, and cognac diamonds come from the Argyle Mine in Western Australia.

The light can only exit in certain ways, so the facets are placed so that the light concentrates and makes the diamond sparkle.