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All lessons Optics22 min

Reflection and Refraction

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01
Hook
02
Explore
03
Formalize
04
Practice
05
Challenge
Interactive simulation
01

Hook

A straw in a glass of water looks snapped in two — but touch it and it's perfectly whole. That same bending trick lets hair-thin glass fibres carry every YouTube video, every WhatsApp message, and every Zoom call across the ocean floor at nearly the speed of light without losing a single bit. How can light bending in a glass of water be the same phenomenon that carries the entire internet?

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Spoilers

Reflection and Refraction — summary and key formula

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The question

A straw in a glass of water looks snapped in two — but touch it and it's perfectly whole. That same bending trick lets hair-thin glass fibres carry every YouTube video, every WhatsApp message, and every Zoom call across the ocean floor at nearly the speed of light without losing a single bit. How can light bending in a glass of water be the same phenomenon that carries the entire internet?

When light crosses from one transparent material into another it changes speed — slowing down in glass or water, speeding up back in air. Any wave that changes speed at a boundary also changes direction. That bending is called refraction. It's why a pool looks shallower than it is, why mirages shimmer above hot roads, and why optical fibres can guide light around corners with no loss at all.

The key idea

Every transparent material has a refractive index n = c/v, where c is the speed of light in vacuum and v is the speed in the material. Air: n ≈ 1.00. Water: n = 1.33. Glass: n ≈ 1.5. Diamond: n = 2.42. The higher n is, the slower light travels and the more it bends. When light tries to leave a denser medium (high n) at a steep angle, it cannot escape — this is Total Internal Reflection (TIR). Optical fibres exploit TIR in a glass core surrounded by slightly less-dense cladding to pipe light signals over thousands of kilometres.

Snell's Law connects angles and refractive indices. For TIR, set θ₂ = 90° to find the critical angle: sinθ_c = n₂/n₁. Glass-to-air: sinθ_c = 1.0/1.5 → θ_c ≈ 41.8°. Any angle inside the glass steeper than 41.8° gives perfect reflection back into the glass — zero loss. Diamond cutters exploit TIR by designing facets so that almost all entering light bounces repeatedly inside before exiting through the top face, maximising sparkle.

The formula

n1sin⁡θ1=n2sin⁡θ2n_1\sin\theta_1 = n_2\sin\theta_2n1​sinθ1​=n2​sinθ2​
  • ·n₁ = refractive index of medium 1
  • ·θ₁ = incident angle measured from the normal
  • ·n₂ = refractive index of medium 2
  • ·θ₂ = refracted angle measured from the normal. The law of reflection (always true): angle of incidence = angle of reflection.