How Total Internal Reflection Occurs: Comparative Multiple Entities, Facts

The total internal reflection of light is the reason why diamond sparkles. We shall explore in detail about how total internal reflection occurs in this article.

Total internal reflection of light occurs when a light ray travels from a denser medium to a rarer medium and makes an angle of incidence greater than the critical angle at the boundary separating the two media. As a result, the light ray gets reflected back completely to the same denser medium without entering the rarer medium.

Formation of mirage, shining of a crack in a glass vessel, transmission of light rays in optical fiber, etc are due to the total internal reflection of light. Furthermore many optical instruments like telescopes, periscopes, binoculars employs glass prisms for total internal reflection.

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How total internal reflection occurs in diamond?

Diamonds are very precious gems that sparkle when light passes through them. Total internal reflection is what happens in it.

how total internal reflection occurs
Total internal reflection in Diamond

The diamond-air interface has a critical angle of 24.4° and that is very low. The facets of the diamond are in such a way that as a light ray enters the diamond; it undergoes multiple total internal reflections as the incident angle for the light ray inside the diamond for each surface is greater than the critical angle. The light ray emerges out of the diamond only when the angle of incidence becomes less than 24.4 degrees.

In addition, by suitably cutting the diamond, multiple internal reflections can be facilitated to increase its sparkle.

How does total internal reflection occur in optical fiber?

Optical fibers are thin, transparent, hollow tube-like wires that are mainly used for transmission of light. Fiber-optics communications use optical fibers.

The refractive index of the medium within the optical fiber must be larger than the surroundings. Light entering a thin optical fiber strikes the inner surface at large angles and suffers total internal reflection. The large incident angle facilitates the ray to travel inside the fiber by undergoing multiple reflections and light emerges out of the optical fiber only at its other end.

In case of optical bundles, the fibers are surrounded by a cladding material whose refractive index is less than the fiber and hence light travelling inside the fiber suffers total internal reflection.

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How does total internal reflection occur in a prism?

Prism is made of glass and the critical angle for the glass-air interface is 42 degrees. Total internal reflection is easily observed in a right-angled isosceles prism. Such a prism contains a right angle and other two angles are same i.e., 45 degrees each.

How total internal reflection occurs in a prism is demonstrated below:

Total internal reflection in prism

The light ray enters perpendicularly through a face of the prism, but once it enters, the incident angle at the inner part of the other face would be 45 degrees which is greater than the critical angle for the glass-air interface. Hence, light ray undergoes total internal reflection and emerges outside the prism through the other face normally.

How is total internal reflection used in binoculars?

Total internal reflection is used in prismatic binoculars to produce a magnified and clear image of the far away objects.

The light ray from the object enters the prism inside the binocular through the lens. The ray on entering the prism is totally reflected inside the prism and emerges out of the prism but enters another prism. There it is again reflected and the finally the light ray reaches the eyepiece.

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How does reflection occur in kaleidoscope?

A kaleidoscope consists of multiple mirrors that result in multiple reflections. The combination of mirrors produces different patterns of the object along with multiple images. Two or more mirrors are arranged in such a position with definite angle of incidence so that multiple reflections are facilitated.

Image Credits – Kaleidoscope – Wikimedia Commons

The mirrors in the kaleidoscope are mostly placed at an angle of 60 degrees with each other.

How do periscopes use total internal reflection?

Persicopes use totally reflecting prisms that turn the light ray by 90 degrees. Totally reflecting prism consists of a right angle and other two angles are equal i.e, 45 degree. Light gets totally reflected in the glass prism.

A ray of light enters perpendicularly through one side of the prism and it is internally reflected at the hypotenuse. The angle of incidence for the light ray at hypotenuse of this right-angled prism is 45 degrees. This angle is greater than the critical angle for the glass-air boundary. The glass-air interface has a critical angle of 42 degrees. After suffering reflection, the light ray emerges through the other side of the prism perpendicularly and then enters the second right-angled prism. The same events happen here and finally the emerging light ray reaches the observer’s eye.

Periscope – Total internal reflection

There is almost no loss in intensity in total internal reflection and hence the obtained images will be bright and clear. Periscopes are used in land and sea warfare, submerged submarine navigation, etc .

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How Total Internal Reflection Occurs: Frequently Asked Questions

What is critical angle?

Critical angle plays a major role for total internal reflection to occur. At the interface separating the denser and the rarer medium, whenever a light ray makes an angle of incidence in the denser medium for which its angle of refraction in the rarer medium is ninety degrees, the measure of that particular incident angle is termed as critical angle. Whenever the angle of incidence becomes greater than this critical angle, total internal reflection takes place.

Image Credits – Total internal reflection – wikipedia

Critical angle for any denser-rarer media interface can be calculated using the Snell’s law of refraction of light. According to the Snell’s law, “The ratio of sine of angle of incidence to the sine of angle of refraction is equal to the ratio of refractive index of the second medium to the refractive index of the first medium”.

sini/sinr=n2/n1

where,

n1 and n2 are the refractive indices of medium 1 and 2 respectively;

i is the angle of incidence;

r is the angle of refraction.

As we know, only those light rays travelling from denser medium to rarer medium undergo total internal reflection. Hence, in the expression for the Snell’s law, the angle of refraction is taken as 90 degree and the corresponding incident angle we obtain is the critical angle.

Give the necessary and sufficient conditions under which total internal reflection occurs.

Total internal reflection happens at any interface separating two media only if the following conditions are satisfied:

  • The light ray should be propagating from a denser medium (a medium with high refractive index) to a rarer medium (a medium with low refractive index).
  • When a light ray moves from denser to rarer medium, the incident angle for the ray at the interface separating the media must be greater than the critical angle for that interface.

Give one application of optical fiber.

Optical fibers are used in medical industry in endoscopy for examining the internal organs of patients.

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