Interference of Electromagnetic Waves: Wave Properties of Light and Thin Film Interference, Slides of Physics

Download Interference of Electromagnetic Waves: Wave Properties of Light and Thin Film Interference and more Slides Physics in PDF only on Docsity! Wave properties of light 1. Interference of two electromagnetic waves 2. Interference of electromagnetic waves in thin films Docsity.com Webassign hint: Two converging lenses having focal lengths of ‘, = 12.5 cm and f, = 18.0 cm are placed a distance d = 49.0 cm apart as shown in the figure below. The image due to light passing through both lenses is to be located between the lenses at the position x = 32.0 cm indicated. fi oe Object Final image t ma | a Tt (a) At what value of p should the object be positioned to the left of the first lens? % [2918.1] cm (b) What is the magnification of the final image? % [2-4.32 Docsity.com From previous lecture: Diverging lens: Converging lens: virtual image of face smaller virtual image of face larger Docsity.com k  Wave phenomena associated with light    Plane polarized   electromagnetic wave  at an instant of time:           vtxEtxEy λ π2sin),( max ),(),(),( portion) field (electric wavesneticelectromag twoofion Superposit 21 txEtxEtxE yy tot y                                  2 cos 2 1 λ π2sin2 λ π2sin λ π2sin),( max maxmax   vtxE vtxEvtxEtxEtoty Docsity.com                                 2 cos 2 1 λ π2sin2 λ π2sin λ π2sin),( )(continuedion Superposit max maxmax   vtxE vtxEvtxEtxEtoty                             2 cos 2 sin4)sin()sin( :magnitude Squared 2 cos 2 sin2)sin()sin( :identitytrictrigonomethefromfollowsresult that thisNote 222 BABABA BABABA             2 cos4 2 cos 2 4 2 1 : wavesEM theofIntensity 21 2 max 0 22 max 0 1    IE c I IE c SI tot avg Time average = 1/2  Constant in time  Docsity.com Two examples of superposed radiation: Interference from refraction and reflection of thin films Young’s double slit ® Docsity.com   λ θsin π λ π 21 mdmrr                                 λ πcosπ2 λ πsin2 π2 λ π2sinπ2 λ π2sin),( 2121 max 2 max 1 max rrftrrE ftrEftrEtPE θsinδ21 drr    intensity maxima occur for   Young’s double slit geometry:  Mathematical analysis of bright fringes:  Docsity.com Intensity pattern at screen for double slit:                λ θsinπcos μ2 4 λ πcos μ2 4 2 0 2 max212 0 2 max d c Err c EI av S Imax  Docsity.com Interference in thin films           vtxEtxEy λ π2sin),( max nf c n cv   ; fn c n cv 1 1 1 1 ;   fn c n cv 2 2 2 2 ;   fn c n cv 3 3 3 3 ;   Interfering transmitted light  Interfering reflected light  Docsity.com Interference between reflected waves:  Recall ‐‐ the behavior of a plane‐polarized electromagnetic wave near the surface  of two materials:  k1  E1  B1  k1´  k2     tEE tEE 11max1 11max1 ωsin ωsin 1 1   rk rk  tEE 22max2 ωsin2  rk 2 2 2ω v k  1 1 1 1 1 ωω v kk     Periodic waves:  E’1  E2  Docsity.com k1  E1  B1  k1´  k2  E’1  E2  Matching electric and magnetic  fields at boundary:  n1  n2  2211 2211 maxmax θcosθcos θcosθcos 11 nn nnEE    2112 2112 maxmax θcosθcos θcosθcos 11 nn nnEE    or  Docsity.com Example of interference with “+”  n1  n2  n3     221max cos BAII  peaks at     π λ )(π 12 2 1 mrrBA  n1< n2< n3  For each surface with n1< n2      E2 = ‐E1   for reflected beam  Docsity.com Example of interference with “”  n1  n2  n1     221max cos BAII  peaks at     π λ )(π 12 2 1 mrrBA  n1> n2  Example of interference with “”     221max sin BAII  peaks at      π λ )(π 2 112 2 1    mrrBA Docsity.com Summary  2 2 0 2 2 0 2 2 2 12at maxima 2 sin4 2at maxima 2 cos4 2222 n mLII n mLII nLL                          Docsity.com