Short Answer

Total Internal Reflection (TIR) occurs only when two specific conditions are met. First, light must travel from a denser medium to a rarer medium such as from glass to air or water to air. Second, the angle of incidence in the denser medium must be greater than the critical angle for that pair of media.

When both these conditions are fulfilled, the light ray does not refract into the rarer medium. Instead, it reflects completely back into the denser medium, producing a bright and perfect reflection.

Detailed Explanation :

Conditions for TIR

Total Internal Reflection (TIR) is a special optical phenomenon that occurs when a light ray travelling inside a denser medium gets completely reflected at the boundary, instead of refracting into the rarer medium. Unlike normal reflection, which happens at any angle, TIR happens only when very specific conditions are satisfied.

TIR is used in optical fibres, binoculars, periscopes, diamond brilliance, and many scientific instruments. It ensures 100% reflection without losing energy, which makes it extremely useful in modern technology.

To understand TIR clearly, we must explore the conditions that make it possible.

First Condition: Light Must Travel From a Denser Medium to a Rarer Medium

The first and most important condition is that light should move from:

• Water → Air
• Glass → Air
• Diamond → Air
• Oil → Air

These are examples where the initial medium has a higher refractive index (denser), and the second medium has a lower refractive index (rarer).

If the direction is reversed (i.e., from air to water), light bends towards the normal and TIR cannot take place under any circumstances.

Why this condition matters:

• When light goes from denser to rarer medium, the refracted ray bends away from the normal.
• As the angle of incidence increases, the refracted ray bends more and more.
• At a certain angle, it bends so much that it travels along the boundary.
• Beyond this angle, the refracted ray no longer exists.

Thus, the direction of light is crucial for achieving TIR.

Second Condition: Angle of Incidence Must Be Greater Than the Critical Angle

The critical angle is the angle of incidence in the denser medium for which the angle of refraction becomes 90° in the rarer medium.

If the angle of incidence is:

• Less than the critical angle → refraction + partial reflection occur
• Equal to the critical angle → refracted ray moves along the boundary
• Greater than the critical angle → total internal reflection happens

This means that the light ray is completely reflected back into the denser medium and no refraction takes place.

The critical angle depends on the refractive indices of the two media:

• Water to air → critical angle ≈ 49°
• Glass to air → critical angle ≈ 42°
• Diamond to air → critical angle ≈ 24°

A smaller critical angle means TIR happens more easily.

Why These Conditions Lead to TIR

To understand why TIR occurs only when both conditions are satisfied, consider the behaviour of light as explained by Snell’s Law:

sin i / sin r = constant

When light travels from denser to rarer medium, the refracted ray bends away from the normal. As the angle of incidence increases, the angle of refraction also increases.

At the critical angle, r = 90°.
If the incident angle increases beyond this point, it becomes impossible for Snell’s law to produce a refracted ray because sin r would have to be greater than 1, which is not possible.

Therefore, the light ray cannot enter the rarer medium and is forced to reflect completely back into the denser medium.

This reflection is called Total Internal Reflection.

Examples Demonstrating the Conditions for TIR

Several real-life situations demonstrate these conditions:

1. Sparkling Diamond
   Diamonds have very small critical angles due to their high refractive index. Light entering a diamond undergoes repeated TIR, producing strong brilliance.
2. Optical Fibre Communication
   Light travels through thin fibres using TIR. The core has a denser medium and the cladding has a rarer medium. Light striking the boundary at greater than the critical angle remains trapped inside.
3. Mirage on a Hot Day
   Layers of warm air near the ground act as rarer mediums. Light travelling from cooler denser layers bends away and eventually undergoes TIR, creating the illusion of water.
4. Shining Water Surface
   At certain angles, underwater objects cannot be seen because the light undergoes total internal reflection.

These examples show that both conditions must be met for TIR to occur.

Importance of Understanding These Conditions

Knowing the conditions for TIR is important because:

• It helps explain natural optical illusions
• It is essential for designing telecommunications equipment
• It improves optical instruments by providing perfect reflections
• It helps engineers design lenses, prisms, and fibre cables
• It is used in medical devices like endoscopes

Understanding these conditions allows us to predict when TIR will occur and how to use it effectively.

Conclusion

The conditions for Total Internal Reflection (TIR) are:

1. Light must travel from a denser medium to a rarer medium.
2. The angle of incidence in the denser medium must be greater than the critical angle.

When these two conditions are fulfilled, light does not refract into the rarer medium. Instead, it reflects completely back into the denser medium. These conditions explain important technologies such as optical fibres and natural effects like mirages.