The control of the trajectory of light is extremely important
Why do we study refraction
Because it is extremely important. Let me give you some reasons for it.
The refraction of light is the phenomenon exploited in the construction of lenses. Lenses are devices that expand our ability to observe the universe, from the very small to the very big!
Without lenses we would not have microscopes to show us that our planet is dominated by micro-organisms such as bacteria, which sometimes are good to us, sometimes are bad. In any case, they dominate this planet for billions of years, and in numbers that are so large that is difficult to imagine.
Furthermore, lenses allow us to build telescopes, needed to admire that hugeness of the universe: the distant planets, stars and galaxies as well as more exotic objects like quasars and supernovas.
Links to biology:
the eye
Even more important and fundamental is the fact that we would not be able to see anything without the lenses inside our eyes, in addition to other devices that increase their refractive power like the cornea and the liquids (humours) inside the eye, which increase a lot the refractive power of the eye.
The cornea is responsible for most of the refractive power of the eye. The rest occurs at the lenses, which are important because of their focusing power. The cornea (in humans) cannot focus, only the lens can, because they are attached to muscles that change its shape in order to increase or decrease refractive power. Our vision under water is blurred because the interface between air and cornea (liquid) that normally causes light to bend is not present . If the cornea is surrounded by water its refractive power is greatly reduced.
evolution of the eye
A basic knowledge of optics is needed to understand the evolution of the eye, which evolved from a bunch of cells that could only sense the present light to the sophistication of the eye we have, that provides very good coloured images. Some animals that are still alive today have much more primitive eyes, which can be similar to a pin-hole camera. A pin-hole camera can be made with a cardboard box and a small hole in one of the sides. Greasy paper is normally used to project the image created by the pin-hole.
The eye has been used as an example of "intelligent design", the idea that only a god can make such a perfect organ. But it is not that perfect. It possesses a blind spot, which the brain manages to disguise very well. Also, the retina has its veins on the side were images form. It would be much better if veins and arteries irrigating the retina were located on the back, although we don´t normally see it because the brain manages to eliminate it from our images.
Optical fibres
Optical fibres have a multitude of applications in science and technology. They are able to conduct light and direct it to where you want it. It is like a pipe for water. In fact there are videos that show how water can also serve the purpose of conducting light. But a very thin fibre made of glass is much more convenient.
In medicine, optical fibres allow to see the interior of living bodies, avoiding the need to cut them. At the same time the take light into the body to illuminate it.
Optical fibres are used for telecommunications; in fact. the backbones of the internet are made of optical fibres that cross the planet in all directions, everywhere, even below the oceans. Information is carried by lasers that can travel thousands of miles below the seas; the y eventually have to be reinforced by especial stations placed along the line. Optical fibres have many advantages of copper wires, because they can transmit much more information and their cost is much lower. Glass is much cheaper than copper; glass is mad of silica that is basically sand. Other advantage of optical fibres is that they don´t get affected by electric and magnetic fields, like copper cables do, which causes interference.
In situation where there are extreme magnetic fields, copper cables cannot function. That happens in the case of MRI (magnetic resonance imaging machines), where fibre optics are used to deliver power, coupled to a photovoltaic cell.
twinkle twinkle little star
There are also some intriguing phenomena that are explained by refraction, like the twinkling of stars. Stars twinkle because of variations on the refractive index of the atmosphere. That is why the largest telescopes are placed on the top of mountains, so that it avoids part of the atmosphere at least.
The temperature of air affects its refractive index, because in a hotter gas he particles move faster and as a result the density is reduced. Lower density implies in lower refractive index. Also, layers of air move t different speeds, so that there is a lot of variation on the refractive index of the atmosphere . Planets don´t twinkle because they are much closer so that they are not seen as points, like the stars, they are extended objects. When you look stars on the telescope, they always appear as dots of light. The advantage of the telescope is that you can see dots that you wouldn’t´t see otherwise. When you look at planets on the telescope they don´t appear as dots but a extended objects. For instance, you can see the rings of Saturn or the moons of Jupiter, as Galileo saw hundreds of years ago.
The implications of refraction for the materials of the future are discussed in this page: the materials of the future - the search for the invisibility cloke .
Shine diamond...
Diamonds shine so much because, due to their high refractive index, the light is internally reflected and return instead of moving across it. This phenomenon is called total internal reflection and is studied in this page: Refraction - IGCSE topics and calculations
Their high refractive index is what confers this extreme beauty, that qualifies them to be used in jewellery.