Definition and Conditions
Definition of Total Internal Reflection: Total internal reflection is a special event that happens when light tries to move from a material where it travels more slowly (like water or glass) into a material where it travels faster (like air), but instead of passing through, the light bounces completely back into the first material. It doesn’t escape at all—it reflects back just like a mirror!
Medium Transition Requirement: For total internal reflection to happen, light must be moving from a material that is optically denser (like water or glass, where light slows down) into a material that is optically less dense (like air, where light speeds up). This means light is going from slow to fast
Angle Condition: This reflection only happens when the angle at which light hits the boundary is bigger than a certain value called the critical angle. If the angle is smaller, some of the light will still go through.
Critical Angle
Definition of Critical Angle: The critical angle is a special angle. It’s the angle of incidence in the denser material that makes the refracted light beam travel exactly along the boundary—neither into the new medium nor back inside. It just slides along the edge.
Surface Travel at Critical Angle: When light hits the surface at the critical angle, it doesn’t go into the new medium. Instead, it skims along the surface, kind of like a stone skipping across water.
Less than Critical Angle: If the angle is smaller than the critical angle, some of the light goes through into the second material, and some might reflect back. It’s a mix of refraction and reflection.
Equal to Critical Angle: If the angle is exactly equal to the critical angle, the light beam travels right along the surface of the two materials—neither going through nor bouncing back.
Greater than Critical Angle: When the angle is greater than the critical angle, all the light is reflected back into the denser medium. None of it goes into the second medium. This is when total internal reflection truly happens.
Critical Angle Dependence: The actual value of the critical angle depends on the optical densities (refractive indices) of the two materials. Different materials give different critical angles.
Critical Angle Formula: We can calculate the critical angle using the formula , where “n” is the refractive index of the denser medium, and “c” is the critical angle. This helps scientists figure out exactly when total internal reflection will occur.
Relationship Between Critical Angle and Refractive Index
Inverse Relationship: There is an opposite (inverse) link between the refractive index of a material and its critical angle. This means that when the refractive index is high, the critical angle becomes small. In other words, as the material gets better at slowing down light, the angle at which light must strike the surface to reflect back completely (instead of bending out) becomes smaller. This makes total internal reflection easier to achieve in materials with a high refractive index.
High Refractive Index Effect: A higher refractive index means that light travels more slowly through the material compared to other materials. When light tries to leave this material and enter a less dense material, it bends more sharply. This bending happens because light is changing speed quickly. As a result, the angle needed for total internal reflection to happen gets smaller, meaning light reflects back even at a lower angle.
Low Refractive Index Effect: A lower refractive index means the material doesn’t slow down the light very much. So, when the light moves from this material into another, it doesn’t bend much. This makes the critical angle larger, meaning the light has to strike the surface at a wider angle in order to reflect completely and not pass into the second material.
Total Internal Reflection at an Interface
Bending Away from Normal: When light goes from a material that is more dense (like glass or water) into one that is less dense (like air), the light bends away from the normal. The normal is an imaginary straight line that stands at 90° to the surface where the two materials meet. Bending away from the normal means the light spreads out more.
Increasing Incident Angle: If you gradually increase the angle at which light hits the surface from inside the denser material, the light bends more and more as it exits. The angle between the refracted light and the normal becomes larger. This happens because light moves faster in the less dense material, so it bends more.
Critical Angle Point: There is a special angle where the light no longer passes into the second material but instead runs along the boundary. This special value is called the critical angle. At this point, the refracted light doesn’t go out—it just skims along the edge of the material.
Beyond Critical Angle: When the angle of incidence is greater than the critical angle, the light doesn’t exit into the second material at all. It gets completely reflected back into the denser material. This total bouncing back of light is what we call total internal reflection. No light passes through the boundary at all.
Angle of Reflection Rule: When light undergoes total internal reflection, it follows the same rule as when it reflects off a mirror. The angle at which the light hits the surface (the incident angle) is exactly the same as the angle it reflects back (the reflection angle). This rule helps us predict where the light will go.
Applications of Total Internal Reflection
Optical Fibres: Optical fibres are very thin threads made of glass or plastic that carry light from one end to the other. The light bounces around inside the fibre instead of escaping, thanks to total internal reflection. This bouncing keeps the light moving efficiently over long distances.
Structure of Fibres: An optical fibre has two main parts. The middle part is called the core, and it has a high refractive index. The outer part is called the cladding, and it has a lower refractive index. This design makes sure that light stays trapped inside the core and keeps bouncing without escaping.
Telecommunications Use: Optical fibres are used to send data for things like internet connections, phone calls, and TV broadcasts. Because total internal reflection keeps the light signal strong, data can travel quickly and clearly, even across oceans and between countries.
Endoscope Function: An endoscope is a tool doctors use to look inside a person’s body. It’s long and bendy and has optical fibres inside that shine light into the body and carry back pictures. The light reflects inside the fibres using total internal reflection so that doctors can see deep inside without surgery.
Medical Use of Endoscopes: Endoscopes are very helpful in medicine because they allow doctors to see inside places like the stomach or lungs without making a big cut. This makes the procedure safer, less painful, and faster for the patient.
Prisms in Periscopes: Periscopes are used to see things that are above or around an obstacle. They contain mirrors or glass prisms that reflect light using total internal reflection. This helps people in submarines or behind walls see things without being seen themselves.
Prisms in Binoculars: Binoculars have prisms inside them that help flip the image so it appears right side up. These prisms use total internal reflection to guide the light properly through the binoculars and show a clear, correct image to your eyes.
Reflective Road Signs: Some road signs are made with materials that reflect light back to drivers at night. These signs use tiny structures that reflect light using internal reflection so that drivers can see the signs clearly when their headlights shine on them.
Visibility Enhancement: Because of total internal reflection, reflective road signs are easier to see in the dark. The light from car headlights hits the sign and reflects straight back to the driver, making the signs brighter and safer to follow at night.
Brilliance of Diamonds: Diamonds look shiny and sparkly because they reflect light inside themselves many times before it comes out. This happens because diamonds have a very high refractive index and a small critical angle, which traps the light and makes it reflect again and again inside the stone.
Mirage Formation: On very hot days, the air near the ground becomes much warmer and less dense than the air above it. This makes the light bend as it passes through the layers of air. Sometimes the bending is so strong that the light reflects, creating a mirage—a fake image like a puddle that isn’t really there.
Illusion on Roads: The shiny spots that look like water on a hot road are not real puddles. It’s actually light from the sky that bends and reflects in the hot air near the ground. This trick of the eyes is caused by total internal reflection and bending of light.
Rainbows and Reflection: Inside raindrops, light bends as it enters and reflects inside the drop. The light may bounce more than once before it exits. Total internal reflection helps the light stay inside the raindrop long enough to split into different colors, which is how we see a rainbow.