Refraction of light at plane surfaces

The angle of incidence for which the angle of refraction is 90°

Step 1: Critical angle occurs when light travels from a denser medium to a rarer medium. Step 2: At the critical angle, the refracted ray grazes along the interface between the two media, making a 90° angle with the normal. Step 3: For angles greater than the critical angle, total internal reflection occurs - no light exits the denser medium. Step 4: The critical angle can be calculated using sin C = n₂/n₁, where n₁ > n₂. Step 5: This concept is crucial for understanding phenomena like mirages and the working of optical fibers.

Light travels from denser to rarer medium and angle of incidence is greater than critical angle

Step 1: Total internal reflection requires two specific conditions to be met simultaneously. Step 2: First condition: Light must travel from a denser medium (higher refractive index) to a rarer medium (lower refractive index). Step 3: Second condition: The angle of incidence must be greater than the critical angle for that particular interface. Step 4: When both conditions are satisfied, no light is transmitted to the second medium - all light is reflected back into the first medium. Step 5: This phenomenon is utilized in optical fibers, diamond cutting, and explains mirages on hot roads.

Total internal reflection due to varying refractive index of air

Step 1: On hot days, air near the road surface becomes very hot and less dense than the cooler air above. Step 2: This creates layers of air with different densities and therefore different refractive indices. Step 3: Light from the sky travels through these layers and gradually bends due to the changing refractive index. Step 4: Eventually, the light undergoes total internal reflection in the hot air layer near the ground. Step 5: This reflected light creates the illusion of water or a mirror-like surface on the road, which we perceive as a mirage.

Total internal reflection

Step 1: Optical fibers are thin strands of glass or plastic designed to transmit light over long distances. Step 2: Light enters the fiber at one end and travels through multiple total internal reflections along the fiber walls. Step 3: The fiber core has a higher refractive index than the surrounding cladding, ensuring light stays trapped inside. Step 4: Due to the small diameter, light rays hit the core-cladding boundary at angles greater than the critical angle. Step 5: This allows light signals to travel long distances with minimal loss, making optical fibers ideal for telecommunications a