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Total Internal Reflection - Definition, Formula, Example, FAQs

Total Internal Reflection - Definition, Formula, Example, FAQs

Vishal kumarUpdated on 02 Jul 2025, 04:38 PM IST

Define total internal reflection using an example.

Consider the case below. A ray of light travels from a watery medium to air. The light ray will be refracted at the point where the two mediums meet. The refracted light ray bends away from the normal as it passes from a medium of a higher refractive index to one of a lower refractive index. The angle of incidence at which the refraction angle is 90 degrees is called the critical angle. The incident ray will reflect back to the medium when the angle of incidence is larger than the critical angle. This is known as total internal reflection.

Total internal reflection critical angel

When Does Total Internal Reflection Occur?

Consider two lights passing through an optically denser media and into an optically rarer material at specific points.

The refraction of light is the phenomenon that causes light to bend off its normal path. This is a unique situation in which the refracted angle exceeds the incident angle.

The above statement describes how increasing the angle of incidence causes the angle of refraction to increase.

There is still a moment where the refraction angle becomes perpendicular. The refracted light will become parallel to the interface as a result of this.

The refracted ray angle of the rarer medium corresponds to the incident ray angle of the denser medium, which is 90°. This is called the critical angle of total internal reflection (c).

The ray returns to the same medium when it is incident on the surface at an angle larger than the critical angle. Total internal reflection refers to the full process of returning a light beam away from a denser medium. So total internal reflection occurs when the incidence angle is greater than the critical angle.

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Conditions for total internal reflection of light

There are two primary factors that influence whether or not the phenomena of total internal reflection occurs. (TIR) is founded on. A little difference in the two circumstances may not yield the desired effect.

There are two prerequisites for total internal reflection:

  1. Light incident at the interface of two different media should prefer to pass from a denser to a rarer medium.
  2. For these two media, a larger angle of incidence is required than the critical angle.

Total internal reflection of light formulas:

Commonly Asked Questions

Q: What is total internal reflection?
A:
Total internal reflection is an optical phenomenon that occurs when light traveling in a denser medium hits the boundary with a less dense medium at an angle greater than the critical angle. In this case, all the light is reflected back into the denser medium, with no light passing through to the less dense medium.
Q: What is the difference between partial and total internal reflection?
A:
Partial internal reflection occurs when some light is reflected and some is refracted at the boundary between two media. Total internal reflection occurs when all light is reflected back into the original medium, with no refraction occurring.
Q: Can sound waves undergo total internal reflection?
A:
Yes, sound waves can undergo total internal reflection. This phenomenon can occur at the boundary between two media with different sound velocities, such as warm and cold layers of air in the atmosphere.
Q: Can total internal reflection occur in a vacuum?
A:
No, total internal reflection cannot occur in a vacuum. It requires two media with different refractive indices, and a vacuum has a refractive index of 1, which is lower than any material medium.
Q: How does total internal reflection affect the apparent depth of a swimming pool?
A:
Total internal reflection can make a swimming pool appear shallower than it actually is. Light rays from the bottom of the pool that would normally reach an observer's eyes at steep angles are totally internally reflected at the water-air interface, reducing the apparent depth of the pool.

Total internal reflection formula

Snell's Law: $n_1 \sin i=n_2 \sin r$
Critical Angle Formula: $\Theta_{\text {crit }}=\sin ^{-1}\left(\frac{n_2}{n_1}\right)$

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Commonly Asked Questions

Q: How is the critical angle calculated?
A:
The critical angle (θc) can be calculated using Snell's law: sin(θc) = n2/n1, where n1 is the refractive index of the denser medium and n2 is the refractive index of the less dense medium.
Q: What is the relationship between the critical angle and the refractive indices of two media?
A:
The critical angle (θc) is related to the refractive indices of the two media by the equation: sin(θc) = n2/n1, where n1 is the refractive index of the denser medium and n2 is the refractive index of the less dense medium. As the ratio n2/n1 decreases, the critical angle decreases.
Q: What conditions are necessary for total internal reflection to occur?
A:
Two conditions must be met for total internal reflection: 1) Light must be traveling from a denser medium to a less dense medium (e.g., from glass to air). 2) The angle of incidence must be greater than the critical angle for the two media involved.
Q: What is the critical angle?
A:
The critical angle is the smallest angle of incidence at which total internal reflection occurs. When light strikes the boundary at exactly the critical angle, it will travel along the boundary between the two media rather than reflecting or refracting.
Q: How does the angle of incidence affect total internal reflection?
A:
For total internal reflection to occur, the angle of incidence must be greater than the critical angle. As the angle of incidence increases beyond the critical angle, all light is reflected back into the denser medium.

Total internal reflection examples

Here are some examples of total internal reflection:

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Total internal reflection in optical fiber

One of the most important applications of total internal reflection is seen in optical fiber. In an optical fiber, the total internal reflection approach is used. The core of the higher refractive index fiber contains the inner component of the fiber. Another layer of glass surrounds all of these fibers. They have a refractive index that is just below that of the lower refractive index. The fibers are protected by a plastic jacket.

When light from one end of the core goes toward the cladding and propagates through it, this is known as back to back total internal reflection. Optical fibers have a lot of uses in the medical field, especially for endoscopy.

Total internal reflection in optical fiber

Define Acceptance angle:

The acceptance angle of an optical fiber is determined by ray optics is the maximum angle of a ray striking the fiber core (against the fiber axis) that allows incident light to be directed by the core. The numerical aperture is defined as the sine of that permissible angle (assuming an incident ray in air or vacuum) and is mostly governed by the refractive index contrast between the core and cladding of the fiber (assuming an incident ray in air or vacuum):

Acceptance angle formula

$\theta_{\text {acc }}=\frac{1}{n_0} \sqrt{n_{\text {core }}^2-n_{\text {cladding }}^2}$

n 0 = refractive index of the medium around the fibre

ncore = refractive index of core

ncladding = refractive index of cladding

θacc = acceptance angle

Diamond:

Total internal reflection in diamond: The incident ray is greater than the critical angle when it falls on every face of the diamond. The diamond's critical value is 23°. This situation is responsible for a diamond's entire internal reflection, which causes it to shine.

Diamond

Mirage:

It's an optical illusion that causes the water layer to appear at short distances in the desert or on the road. Total internal reflection, which happens as a result of atmospheric refraction, is an example of a mirage.

Mirage

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NCERT Physics Notes:

Commonly Asked Questions

Q: Can total internal reflection occur when light travels from air to water?
A:
No, total internal reflection cannot occur when light travels from air to water. It only happens when light travels from a denser medium (like water) to a less dense medium (like air).
Q: How does a fiber optic cable work?
A:
Fiber optic cables use the principle of total internal reflection to transmit light signals over long distances. The light travels through a core of glass or plastic surrounded by a cladding with a lower refractive index, causing the light to repeatedly reflect off the inner walls of the fiber without escaping.
Q: What happens to the intensity of light during total internal reflection?
A:
During total internal reflection, 100% of the light is reflected back into the original medium. There is no loss of intensity due to transmission or absorption at the boundary, making it an extremely efficient reflection process.
Q: Why does a diamond sparkle more than glass?
A:
Diamonds sparkle more than glass because they have a higher refractive index, which results in a smaller critical angle. This means that more light undergoes total internal reflection within the diamond, leading to increased brilliance and sparkle.
Q: How does total internal reflection differ from regular reflection?
A:
Total internal reflection occurs only at the interface between two media when light travels from a denser to a less dense medium above a critical angle. Regular reflection can occur at any angle and at any interface, but some light is usually transmitted as well.

Frequently Asked Questions (FAQs)

Q: Can total internal reflection be used to create invisible materials?
A:
While true invisibility is not possible, total internal reflection can be used to create materials that are highly transparent or that bend light in unusual ways. For example, some types of metamaterials use precisely designed structures that manipulate light through processes including total internal reflection to achieve unusual optical properties.
Q: How does total internal reflection affect the design of light pipes?
A:
Light pipes use total internal reflection to transport light from a source to a desired location with minimal loss. The design of light pipes considers factors like material refractive index, pipe geometry, and surface quality to maximize the efficiency of light transmission through total internal reflection.
Q: How does total internal reflection contribute to the efficiency of solar cells?
A:
Some advanced solar cell designs use textured surfaces or specialized coatings that promote total internal reflection within the cell. This traps light inside the solar cell for longer, increasing the chance of absorption and improving overall efficiency.
Q: Can total internal reflection be used to create optical illusions?
A:
Yes, total internal reflection can be used to create various optical illusions. For example, a clear object with the right shape and refractive index can appear to vanish when submerged in a liquid with a matching refractive index, due to the absence of reflection or refraction at the interface.
Q: How does total internal reflection affect the design of retroreflectors?
A:
Retroreflectors, such as those used in road signs and safety equipment, often use a combination of total internal reflection and regular reflection to return light directly back to its source. The precise geometry of the reflector ensures that light undergoes the necessary reflections to achieve this effect.
Q: What is the relationship between total internal reflection and the critical angle for different colors of light?
A:
Due to dispersion, different colors of light have slightly different refractive indices in a material. This means that the critical angle for total internal reflection can vary slightly for different wavelengths, potentially leading to some color separation effects.
Q: How does total internal reflection affect the design of solar concentrators?
A:
Some solar concentrators use total internal reflection to guide and concentrate sunlight onto a smaller area of solar cells. This can increase the efficiency of solar panels by allowing them to capture light from a wider area.
Q: What is the difference between total internal reflection and total external reflection?
A:
Total internal reflection occurs when light travels from a denser to a less dense medium at an angle greater than the critical angle. Total external reflection is a term sometimes used to describe the near-perfect reflection of certain wavelengths by multi-layer dielectric mirrors, which is a different phenomenon.
Q: Can total internal reflection be used to measure the refractive index of a material?
A:
Yes, the phenomenon of total internal reflection can be used to measure the refractive index of a material. By determining the critical angle between the material and a reference medium (often air), the refractive index can be calculated using the relationship sin(θc) = n2/n1.
Q: What is the role of total internal reflection in the creation of mirages?
A:
While mirages are primarily caused by refraction, total internal reflection can play a role in some types of mirages. In a superior mirage, for example, light can be trapped between layers of air through a process similar to total internal reflection, creating inverted images.
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