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# Reflection and refraction Fermat's principle - ctaps

Reflection and refraction Fermat's principle - ctaps

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<strong>Fermat's</strong> <strong>principle</strong><strong>Fermat's</strong> <strong>principle</strong>"The actual path between two points taken by abeam of light is the one which is traversed in theleast time.""Light, in going between two points, traverses theroute having the smallest optical path length."OPD = n α d= index of <strong>refraction</strong> × distance travelled

Huygens’ PrincipleHuygens’ PrincipleIn the 17th Century, Christiaan Huygens (1629–1695) proposed what we now know as Huygens’Principle, one of the fundamental concepts ofwaves <strong>and</strong> wave optics.A typical statement of the <strong>principle</strong> is “every pointon a wavefront acts as a source of a newwavefront, propagating radially outward.”

REFLECTIONθ = θi r

REFRACTION

Bending Light: RefractionAs light passes from one transparent medium toanother, it changes speed, <strong>and</strong> bends. How muchthis happens depends on the refractive index ofthe mediums <strong>and</strong> the angle between the light ray<strong>and</strong> the line perpendicular (normal) to the surfaceseparating the two mediums (medium/mediuminterface). Each medium has a different refractiveindex. The angle between the light ray <strong>and</strong> thenormal as it leaves a medium is called the angle ofincidence. The angle between the light ray <strong>and</strong> thenormal as it enters a medium is called the angle of<strong>refraction</strong>.

Snell's LawIn 1621, a Dutch physicist named Willebrord Snell(1591-1626), derived the relationship between thedifferent angles of light as it passes from one mediumto another. When light passes from one medium toanother, it bends according to Snell's law which states:n sin θ = n sin θi i r rwhere:n i is the refractive index of the medium the light is leaving,θ i is the incident angle between the light ray<strong>and</strong> the normal to the medium to medium interface,n r is the refractive index of the medium the light is entering,θ r is the refractive angle between the light ray<strong>and</strong> the normal to the medium to medium interface.

Critical AngleLight bends toward the normal when the lightenters a medium of greater refractive index,<strong>and</strong> away from the normal when entering amedium of lesser refractive index.As you approach the critical angle the refractedlight approaches 90° <strong>and</strong>, at the critical angle,the angle of <strong>refraction</strong> becomes 90° <strong>and</strong> thelight is no longer transmitted across themedium/medium interface. For angles greaterin absolute value than the critical angle, all thelight is reflected. This is called total internalreflection.

At θ c : n1sin θc= n2sin 90 °sinθθcc==nn21sin−nn1 21