Geometrical optics. 3.1 Reflection and Refraction. Wave front. Light waves. Reflection

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1 3. Reflectin and Refractin Gemetrical Optics Reflectin Refractin Ttal Internal Refractin Dispersin Gemetrical ptics In gemetrical ptics light waves are cnsidered t mve in straight lines. This is a gd descriptin as lng as the waves d nt pass thrugh small penings (cmpared t λ) Christian Huygens Light waves Wave frnt Rays are perpendicular t wave frnts perpendicular t wave frnts Rays are nt physical entities but are a cnvenient representatin f a light wave. (surfaces with cnstant phase - e.g. maxima) Reflectin Tw general types f reflectin Specular reflectin Diffuse reflectin Mst f gemetric ptics deals with specular reflectin. Hwever, mst f the time ambient lighting is due t diffuse reflectin. Specular reflectin Flat surface Light reflected in ne directin Diffuse reflectin Rugh surface Light reflected in all directins

2 Transmissin and Reflectin at an interface What are sme examples f these prcesses in this picture. Reflectin Incident wave Transmissin Absrptin x Specular Reflectin Diffuse reflectin (scattering) medium medium Transmissin Absrptin Law f Reflectin The angle f reflectin equals the angle f incidence ' = Full length mirrr A 6 ft tall man wants t install a mirrr tall enugh t see his whle bdy. Hw tall a mirrr is needed? h ½h ½h h Angle f incidence Angle f reflectin Reflecting surface h mirrr = ½ (h + h ) = ½ (6) =3 ft Multiple reflectins Fr multiple reflectins use the law f reflectin fr each reflecting surface. Mirrr -Dimensinal Crner reflectr Mirrr 90- perpendicular mirrrs reflect a light beam in a plane perpendicular t bth mirrrs back alng the ppsite directin we want t shw that = 90 + = 90

3 Crner reflectrs n the mn used t measure the distance t the earth by measuring the rund trip time f light. Refractin Refractin is the bending f light when it passes acrss an interface between tw materials. Due t the differences in the speed f light in different media. Speed f light in a medium Excites scillatin f electrns in medium Wave in vacuum c v Transmissin acrss an interface The speed f the wave changes. The frequency remains the same. The wavelength changes Superpsitin f waves leads t slwer speed in the medium v, cmpared t the speed f light in vacuum. c. Index f refractin c n = v Refractin and Reflectin The light beam (3) is refracted at the interface. 3

4 Ging frm air t glass Snell s Law f Refractin n sin = n sin Ging frm glass t air n sin = n sin n < n > n > n < (sin increases with ) Example. Find the angle f refractin fr an angle f incidence f 30 in ging frm air t glass (n glass =.5) n sin = n sin nsin sin = n.00(sin30) = = = arcsin(0.33) = 9.3 Shw that light ging thrugh a flat slab is nt deviated in angle. First interface Example.4 n sin = n sin Secnd interface angle f incidence = n sin = n sin 3 3 then nsin = nsin 3 3 Angle is the same but beam displaced since n =n 3 = 3 Huygen s Principle Huygen s Picture f a Plane wave All pints in a given wave frnt are taken as pint surces fr the prductin f spherical secndary wavelets which prpagate in space. After sme time the new wave frnt is the tangent t the wavelets. 4

5 Huygen s Picture f a Spherical wave Huygen s Explanatin f Reflectin therefre incidence = reflectin tw sides and an angle equal similar triangles = Huygen s explanatin fr Refractin new wave frnt L Lsin = v t Lsin = v t sin sin v = v sin = sin v v n sin =n sin Fig. -4b, p.74 Ttal Internal Reflectin Ttal Internal Reflectin When the angle f refractin equals r exceeds 90 All the light is internally reflected 5

6 Optical Fiber -Light Pipe An ptical fiber (light pipe) cnfines the light inside the material by ttal internal reflectin. If the refractive index f the fiber is.5 what is the smallest angle f incidence pssible when the light pipe is in air. n sin = n sin = 90 n sin90 (.0)(.0) sin = = = 0.66 n.5 n =.00 n =.5 = arcsin(0.66) = 4 must be > 4 Fiber ptics are used extensively in cmmunicatins. Telephne, Internet, The high frequency f light (cmpared t micrwaves) allws it t be switched rapidly and carry mre infrmatin. Fiber Optics A diamnd sparkles due t ttal internal reflectin Diamnd has a high refractive index n =.4 allwing ttal internal reflectin ccurs mre readily Dispersin Dispersin is the separatin f light with different clrs due t the wavelength dependence f the index f refractin f a prism. The diamnd must be cut prperly = 4 Wavelength dependence f n Different clrs are refracted by different angles in a prism Fr mst materials n increases with decreasing wavelength Highest in the blue regin Lwest in the red regin 6

7 Dispersin f light by a prism Example. A prism f crwn glass refracts light nrmally incident n ne surface. Fr = 40 find the angle between the refracted red and vilet light. vilet n =.538 red n =.56 =40 n=.00 n =40 n sin = nsin sin = n sin red = arcsin( nred sin) = arcsin(.56 sin40) = vilet = arcsin( nvilet sin) = arcsin(.538 sin40) = 8. 3 =4.3 0 Rainbw The shape f the rainbw is due t parallel beam f sunlight light reflected and refracted frm raindrps at a special angle (rainbw angle f 40-4 ) The clrs f the rainbw are due t dispersin f the light. A rainbw is seen n a rainy day when the sun is t yur back, lw in the hrizn (less than 4 abve the hrizn) A secnd rainbw is ften seen with the rder f clrs reversed. Dispersin f light by a rain drp Three interfaces A) Refractin B) Reflectin C) Refractin A) Vilet light is refracted mre but gives a smaller rainbw angle B) C) 7