Applications of Total Internal Reflection

A mirage is an optical illusion seen on hot roads or in deserts where distant objects appear reflected from water-like surfaces.

An optical fibre is a thin, transparent fibre of glass or plastic that transmits light signals using repeated total internal reflection.

1. Air near the hot ground is less dense and has a lower refractive index than the cooler air above it.
2. Light from a distant object travels through layers of air of gradually decreasing refractive index.
3. The ray bends away from the normal continuously and may finally undergo total internal reflection before reaching the observer.
4. The observer traces the ray backwards and feels that the image is formed below the object, as if reflected by water.

Real-life analogy

A hot road on a summer afternoon may appear wet from a distance because the eye interprets the bent light path as a reflected image.

Diamonds appear exceptionally bright because light entering them undergoes repeated total internal reflections before emerging.

Cause:

• Diamond has a high refractive index.
• Its critical angle is very small, so light remains trapped inside for multiple reflections.
• The cut of a diamond is designed to maximise internal reflection and brightness.

1. Totally Reflecting Prism: A totally reflecting prism uses total internal reflection instead of a silvered mirror surface to change the direction of light.
2. Use in Binoculars: Prisms in binoculars deviate light and help produce an erect image while keeping the instrument compact.
3. Use in Periscopes: Two right-angled prisms can change the path of light and help a person see over obstacles.
4. 90° and 180° Deviation: The source material notes that suitable prisms can bend light through 90° or 180° and can also invert images in optical instruments.

Advantages over ordinary mirrors

Structure of Optical Fibre

An optical fibre generally has the following parts:shaalaa

• Core: Inner transparent region through which light travels.
• Cladding: Outer optical layer with a lower refractive index than the core.
• Buffer coating / protective jacket: Protective outer covering that gives mechanical strength.

Working Principle

When light enters the fibre within a suitable range of angles, it undergoes repeated total internal reflections at the core-cladding boundary and continues to travel through the fibre with small loss.

Conditions needed

• The refractive index of the core must be greater than that of the cladding.
• The light must enter the fibre within the acceptance limit so that total internal reflection continues.

Key Features

• A very large bandwidth is possible.
• Attenuation is low.
• Signal transmission is fast and efficient.
• Optical fibres are light in weight and flexible.
• They are not affected by electromagnetic interference.

• Telecommunication and internet data transmission.
• Audio and video signal transfer.
• Medical endoscopy and internal imaging.
• Communication cables with low transmission loss.

Light Pipe Analogy

An optical fibre may be thought of as a “light pipe” that guides light through repeated reflections inside a narrow path.

Acceptance Angle

The acceptance angle is the maximum angle with the fibre axis at which light can enter the fibre and still propagate through it by total internal reflection.

Numerical Aperture

Numerical aperture measures the light-gathering ability of an optical fibre.

A larger numerical aperture means the fibre can accept light over a wider range of incident directions.

• Acceptance angle for an optical fibre is defined as the maximum angle of incidence at the interface of the medium μ = n₁ and the core μ = n₂ for which the light ray enters and travels along the optical fibre.
• The sine of the acceptance angle is known as the numerical aperture (NA) of the optical fibre.

Derivation steps:

1. Apply Snell’s law at interface AB:
   n₁ sin⁡ i_max = n₂ sin ⁡r_max
   So,
   sin⁡ r_max = \[\frac {n_1}{n_2}\]sin⁡ i_max   ...(i)

2. Apply Snell’s law at interface BC:
   n₂ sin⁡(90^∘ − r_max) = n₃ sin⁡90^∘
   So,
   cos⁡ r_max = \[\frac {n_3}{n_2}\]   ...(ii)

3. Square and add equations (i) and (ii):
   \[\sin^2r_{\max}+\cos^2r_{\max}=\frac{n_1^2}{n_2^2}\sin^2i_{\max}+\frac{n_3^2}{n_2^2}\]
   Using sin⁡² r_max + cos^⁡2 r_max = 1, this gives:
   1 = \[\frac{n_1^2}{n_2^2}\sin^2i_{\max}+\frac{n_3^2}{n_2^2}\].

4. \[\sin^2i_{\max}=\frac{n_2^2-n_3^2}{n_1^2}\]
5. \[i_{\max}=\sin^{-1}\left[\frac{\sqrt{n_2^2-n_3^2}}{n_1}\right]\]