Transcription of 3.1 Reflection and Refraction - University of California ...
1 Reflection and Refraction Geometrical Optics Reflection Refraction Total Internal Refraction DispersionChristian HuygensGeometrical opticsIn geometrical optics light waves are considered to move in straight is a good description as long as the waves do not pass through small openings (compared to ) light waves(surfaces with constant phase - maxima) perpendicularto wave frontsRays are not physicalentities but are aconvenient representationof a light frontRays are perpendicular to wave frontsReflection Two general types of Reflection Specular Reflection Diffuse Reflection Most of geometric optics deals with specular Reflection . However, most of the time ambient lighting is due to diffuse reflectionDiffuse reflectionFlat surfaceLight reflected in one directionRough surfaceLight reflected in all directions2 Transmission and Reflection at an interfaceTransmissionReflectionAbsorptio nxIncident wavemedium 1medium 2 Specular ReflectionDiffuse Reflection (scattering)TransmissionAbsorptionWhat are some examplesof these processes in this of ReflectionThe angle of Reflection equals the angle of incidenceAngle of incidenceAngle of Reflection '11 = Reflecting surfaceFull length mirrorA 6 ft tall man wants to install a mirror tall enough to see hiswhole body.
2 How tall a mirror is needed?h1h2 h1 h2hmirror= (h1+ h2) = (6) =3 ftMultiple reflections For multiple reflections use the law of Reflection for each reflecting Corner reflector2 perpendicular mirrors reflect a light beam in a plane perpendicular to both mirrors back along the opposite direction 1 1 2 2we want to show that 2190o = 90- 1 Mirror 2 Mirror 1 1+ 2 = 90o3 Corner reflectors on the moon used to measure the distance to the earth by measuring the round trip time of light . Refraction Refraction is the bending of light when it passes across an interface between two materials. Due to the differences in the speed of light in different of light in a mediumWave in vacuumExcites oscillation of electrons in mediumSuperposition of waves leads to slower speed in the medium v , compared to the speed of light in vacuum. of refractionc v Transmission across an interfaceThe speed of the frequency remainsthe wavelength changesRefraction and ReflectionThe light beam (3) is refracted at the s Law of Refraction112 2n sinn sin = n2 > n1 2 < 1(sin increases with )Going from air to glassGoing from glass to airn2 < n1 2 > 1112 2n sinn sin = Example the angle of Refraction foran angle of incidence of 30oingoing from air to glass (nglass= )112 2n sinn sin = 1122nsinsinn = (sin30) ( ) ==Example 2n sinn sin = Show that light going througha flat slab is not deviated in interfaceSecond interfaceangle of incidence = 22233nsinnsin = then113 3nsinn sin = since n1=n3 1= 3 Angle is the same but beamdisplacedHuygen s Principle All points in a given wave front are taken as point sources for the production of spherical secondary waveletswhich propagate in space.
3 After some time the new wave front is the tangentto the s Picture of a Plane wave5 Huygen s Picture of a Spherical waveHuygen s Explanation of Reflection 1= 1two sides andan angle equal similar triangles incidence= reflectionthereforeHuygen s explanation for Refraction n1sin 1=n2sin 2 Lsin 1= v1tLsin 2= v2t121211sinsinvv = Lnew wave front2121vvsinsin= Fig. 22-24b, Internal ReflectionWhen the angle of Refraction equals or exceeds 90oAll the light isinternally reflectedTotal Internal Reflection6 Optical Fiber - light PipeAn optical fiber ( light pipe) confines the light inside thematerial by total internal Reflection . If the refractive index of the fiber is what is the smallest angle of incidencepossible when the light pipe is in 1 2= 90112 2n sinn sin = 211nsin90( )( ) ===o1arcsin( ) 41 == 1 must be > 41oFiber OpticsFiber optics are used extensively in communications. Telephone, Internet, The high frequency of light (compared to microwaves) allows it to be switched rapidly and carry more diamond sparkles due to total internal reflectionDiamond has a high refractive index n = allowing total internal Reflection occurs more readilyThe diamond must be cutproperly = 41o Dispersion Dispersion is the separation of light with different colors due to the wavelength dependence of the index of Refraction of a dependence of nFor most materialsn increases with decreasing wavelengthHighest in the blue regionLowest in the red regionDifferent colors are refracted by different angles in a prism7 Dispersion of light by a prismExample.
4 A prism of crown glass refracts light normally incident on one surface. For = 40o find the angle between the refracted red and violet light . ) ()sinnarcsin(== = 1=40on1n= = 1 2violet n1= red n1= = ) ()sinnarcsin(== = 21sinsinn = = rainbow is seen on a rainy day when the sun is to your back,low in the horizon (less than 42oabove the horizon)A second rainbow is often seen with the order of shape of the rainbow is due to parallel beam of sunlight lightreflected and refracted from raindrops at a special angle (rainbow angle of 40o-42o)The colors of the rainbow are due to dispersion of the of light by a rain dropThree interfacesA) RefractionB) ReflectionC) RefractionA)B)C)Violet light is refracted morebut gives a smaller rainbow angl
