Total internal reflections and its applications

A complete reflection of a beam of light from the surrounding surfaces back into a medium such as water or glass is known as total internal reflection. When the angle of incidence exceeds a particular limiting angle, known as the critical angle, the phenomena happen. Total internal reflection occurs when a ray of light from a medium with a higher index of refraction approaches the other medium at an angle of incidence larger than the critical angle at the boundary between two transparent media. The critical angle when the mediums are water and air is 48.5o . Because refraction indices are wavelength dependent, the critical angle (and so the angle of total internal reflection) varies slightly with wavelength and, thus, with colour. Both refraction and reflection occur in different quantities at all angles less than the critical angle.

Glass prisms are used in binoculars, periscopes, telescopes, and other optical equipment because they may be curved to achieve total internal reflection. Multiple total internal reflection in glass or plastic rods or fibres can carry light beams along long, twisting routes. 

Reflection of light

When a ray of light strikes a smooth polished surface and bounces back, this is referred to as light reflection. The incident light ray is said to be reflected off the surface when it lands on it. The ray that rebounds back is called the reflected ray. And the perpendicular drawn on a reflective surface is known as normal. 

Laws of reflection

1. The incident ray, reflected ray and the normal should lie on the plane i.e., the reflecting surface

2. The angle made by the incident ray with the normal should be equal to the angle made by the reflected ray with the normal.

Refraction of light

The bending of a wave as it travels from one medium to another is known as refraction. The difference in density between the two substances causes the bending.

When light passes through glass, it slows down and shifts its course slightly. The refracted light bends more towards the normal line as it goes from a less dense solid to a denser substance. The light beam does not refract as it approaches the barrier in a direction that is perpendicular to it, despite the change in speed.

Total internal reflection:

Let us consider a ray of light travelling from water to air. The light ray will be refracted at the separation point of the two media. The refracted light ray bends away from the normal as it passes from the water towards the air. The incident ray of light is refracted in such a way that it passes down the water’s surface at a given angle of incidence. The angle of refraction is 90o. When the angle of incidence is larger than the critical angle the light ray gets reflected back to the denser medium. This behaviour is known as total internal reflection.

Formulas related to total internal reflection

• The formula relating the ratio of refractive indices of the mediums and the angle of incidence and refraction is:

n1 / n2=sin r / sin i

Where, n1, n2 are the refractive indices of medium 1 and medium 2 respectively, i is the angle of incidence and r is the angle of refraction.

• The formula that will give us the critical angle for a pair of media is:

sinθ =n2 / n1

Where, is the critical angle.

Conditions required for total internal reflection

The conditions that are required for total internal reflection to take place are:

1. The ray of light must be travelling from the denser media to a rarer media.

2. The angle made by the incident ray with the normal should be greater than the critical angle for that pair of media.

Applications of total internal reflection:

1. Telecom services: ISPs (Internet Service Providers) rely primarily on telecommunication services to supply us with internet connectivity. Originally, broadband cables were used to connect homes and businesses to the internet, but optical fibre cable is becoming more prevalent. It works on the principle of total internal reflection and can deliver speeds up to 100 times faster than typical broadband connections. When you needed to upgrade your broadband connection for more data bandwidth (data speed), you had to upgrade the wires as well. However, with optical fibre cables, you can theoretically transfer a large amount of data (speeds in Petabytes) on the same cables, and the speed is only limited by your ISP and data plan.

2. Diamond cutting: When a jeweller grinds a diamond, he ensures that the surface is ground at a 23-degree angle so that the light entering the diamond is internally reflected and the diamond shines. The higher the diamond’s lustre, the higher its market value.

3. Mirage formation: we may have seen in movies that there is a mirage of an oasis in the desert (basically a small pond in the desert). For a long time, pedestrians in desert locations have been perplexed by mirages. When the light from an actual oasis is completely internally reflected in the air, mirages are created. Deserts are extremely hot, with the air near the ground being significantly warmer than the air above it. Internal reflection occurs as a result of a difference in the refractive index of the heated and relatively cooler air.

Conclusion

Total internal reflection is a phenomenon that is unconsciously involved in numerous aspects of our lives and is the source of a variety of applications in our daily lives.