Optics. n n. sin. 1. law of rectilinear propagation 2. law of reflection = 3. law of refraction

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1 Optics What is light? Visible electromagetic radiatio Geometrical optics (model) Light-ray: extremely thi parallel light beam Usig this model, the explaatio of several optical pheomea ca be give as the solutio of simple geometric problems.. law of rectiliear propagatio. law of reflectio = 3. law of refractio The icidet ray, the ormal ad the reflected ray, or refracted ray lie i the same plae. All the agles are measured from the ormal! *** All these laws ca be deduced from a sigle commo priciple! Fermat-priciple si c si c The priciple of shortest time : out of the geometrically possible paths, light will travel alog the oe that requires the shortest time to pass.

2 π si si crit. si crit. If β > β crit. Total reflectio core > claddig Applicatio e.g.: Optical fiber (edoscopy), refractometry ***

3 Image formatio by simple curved surface (sphere with radius r): si si The power (refractive stregth): o i r D Applicatio: for the huma eye (ext week) e.g. the power of corea medium r mm - D dpt air 0,37 48 corea 7,7,37 *** Image formatio by two curved surfaces (radii r ; r ) (thi les approximatio): Les equatio ad les-makers equatio: o i f (, ) r r 3

4 Image formatio by leses Simple magifier We have to compare two cases: eye looks at the O object. without les from the covetioal ear poit (a 5 cm), uder the agle of. with les from the distace o, uder the agle of I virtual image Agular magificatio: N ta ta ad we use o f i 4

5 I the case of simple magifier: O ta N o ta O a Two possible aswers: I. if i = a tha II. if i = tha a o a f i a N +, f a N f I the I. case eye looks at the virtual image with accommodatio, i the II. case without accommodatio, eye is focused at ifiity, thus o = f. *** Les systems () microscope Without accommodatio, eye is focused at ifiity. Agular magificatio of microscope: N ta ta da f f 5

6 Les systems () power (refractive stregth) How high the collective focal legth of two close juxtaposed leses is L (f ), L (f )? Let s apply the les equatio for O as a virtual object. Dcoll. D D f f f f f f collective coll. I such cases powers are added. Uits [/m], dioptre, [dpt]. Applicatio e.g.: glasses, cotact leses. *** There are pheomea that caot be explaied by this model. 6

7 Iterferece (two or more waves meet) the most importat pheomeo i coectio with waves E.g. water wave : it ca be observed directly. Because it chages slowly eough (low frequecy, f ) ad the typical (wave) size is large eough (log wavelegth, ). Light waves are differet. Microscopic (short wavelegth, λ); quick chage (high frequecy, f ) At certai coditios patters ca be formed, which do t chage i time, ad their size is much larger tha the wavelegth,. Icoheret ad coheret waves Rise of coheret waves is cotrolled i space ad time, they are sychroized somehow. 7

8 Physical or wave optics (other model) Its bases: HuygesFresel-priciple Accordig to the Huyges priciple, elemetary waves origiate from every poit of a wavefrot, ad the ew wavefrot is the commo evelope of these elemetary waves. The laws of rectiliear propagatio, the reflectio ad refractio ca be described by this model as well. Fresel supplemeted this by observig that the superpositio priciple is also i effect durig the formatio of the ew wave frot, which is othig else tha the quatitative formulatio of the empirical fact that waves will propagate through each other without disturbace. Typical experimet ad patter of light iterferece Youg s double slit experimet (diffractio) The places of costructive ad destructive iterferece are determied by the differece i phase (). 8

9 At a certai place the vibratioal states are demostrated by rotatig vectors: The amplitude of the et vibratio (A resultat ) is give by the vector sum of the compoets (A). Our eyes are sesitive to the light-power (P), that is proportioal to the square of the amplitude. Thus A resultat P res., ad A res. = A + A hece P res. P + P. Resultat (A resultat ) of two vectors (A, A ), or the square of it, if the agle betwee them is : P A resultat = A + A A A cos(- ) (cosie theorem) P A resultat = A + A + A A cos If A = A = A, tha A resultat = A ( + cos) 9

10 The differece i phase () is determied by the relatio of differece i path legth (s) ad the wavelegth (). If L >> d, the differece i path legth s = dsi. The differece i phase is give as: s d si d ta d x L Demostratio: Maxima ca be observed at places correspod to = k or s = k; k = 0,,, coditio. Applicatios: determiatio of the resolvig power of microscopes, 0

11 Light is electromagetic wave thus ca be polarized trasversal liearly polarized light or plae polarized light But elliptically polarized light also exists. Optical aisotropy E.g. i a aisotropic matter the speed of a suitably liearly polarized light depeds o the directio of propagatio. The reaso of it is coected to the structure of matter. Cosequeces, applicatios: double refractio, polarizatio microscope