Refractive Index, Critical Angle & Total Internal Reflection
Calculate refractive index, critical angle for total internal reflection, and the apparent depth of objects in water. Essential for A-level physics optics.
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Refractive Index Guide
What do I need to know about Snell's Law and Refractive Index?
Snell's law: n₁ sin θ₁ = n₂ sin θ₂. Refractive index of medium 2 relative to medium 1: n = sin θ_i / sin θ_r (when going from medium 1 to medium 2, with medium 1 being air/vacuum). The refractive index of a medium: n = c / v where c = speed of light in vacuum (3×10⁸ m/s) and v = speed of light in the medium. Air: n ≈ 1.0003 (effectively 1). Water: n ≈ 1.33. Glass: n ≈ 1.5. Diamond: n ≈ 2.42. Higher n means light slows more and bends more on entering the medium.
What do I need to know about Critical Angle and Total Internal Reflection?
When light travels from a denser medium to a less dense medium, it bends away from the normal. At the critical angle θ_c, the refracted ray travels along the boundary (90° to normal). Above θ_c: total internal reflection — all light is reflected back inside the denser medium. sin(θ_c) = n₂/n₁ = 1/n for glass-to-air. Diamond (n=2.42): θ_c = arcsin(1/2.42) = 24.4°. Very small critical angle means most light is totally internally reflected — this is why cut diamonds sparkle. Optical fibres: light is repeatedly totally internally reflected along the fibre's core, allowing it to travel enormous distances with minimal loss, which is the basis of modern telecommunications.
What should I know about Apparent Depth?
Objects in water appear shallower than they really are due to refraction. Apparent depth = real depth / n. Water (n=1.33): a fish at 2m real depth appears at 2/1.33 = 1.50m. This apparent depth effect is why swimming pools look shallower than they are — a 2m deep pool appears to be approximately 1.5m deep from the surface. The effect explains the apparent bending of a straw in a glass of water — the submerged part appears displaced because light from it refracts at the water-air interface.
What should I know about Applications of TIR?
Optical fibres: core glass has higher n than cladding glass. Light entering within the acceptance cone is totally internally reflected repeatedly along the core. Monomode fibres (core 8-10μm): carry a single light mode, used for long-distance telecoms. Multimode fibres (core 50-62.5μm): multiple modes, used for shorter distances (local area networks). Endoscopes: flexible bundles of optical fibres transmit images from inside the body. Retroreflectors: cat's eyes in road markings and road signs use tiny embedded glass spheres that reflect headlight beams directly back toward the driver, making them visible at night without needing their own power source.