LECTURE 23: LIGHT Propagation of Light Reflection & Refraction Internal Reflection Propagation of Light Huygen s Principle Each point on a primary wavefront serves as the source of spherical secondary wavelets Advance with speed and frequency equal to those of the primary wave Primary wavefront at some later time is the envelope of these wavelets Secondary Secondary Point source wavelet wavelet Plane wave Spherical wave Point source 1
Propagation of Light Fermat s Principle The path taken by light traveling from one point to another is such that the time of travel is a minimum Constant speed Minimize distance traveled Two different speeds Minimize distance traveled at the slower speed Fermat s Principle What's the fastest path to the ball knowing you can run faster than you can swim? This one is better Not the quickest route 11/17/18 8 2
Index of Refraction The speed of an electromagnetic wave is different in matter than it is in vacuum Why?? From Maxwell s eqns in vacuum: How are Maxwell s equations in matter different? e 0 e, µ 0 µ Generally increased by the presence of matter especially e => Speed of light in matter v related to the speed of light in vacuum c by: v medium = n = index of refraction of the material c = c n = c n medium v ε = κ > 1 ε 0 1 µ 0 ε 0 Dielectric constant Index of Refraction Monochromatic: One wavelength Chromatic Dispersion: spreading of light according to its wavelength Medium Index of Refraction n vacuum exactly 1 air (STP) 1.00029 H 2 O (20 o C) 1.33 crown glass 1.52 diamond 2.42 3
What Changes When Passing Between Mediums? f or l? l. f stays the same Light incident on atoms in a medium Atoms generally absorb and re-radiate at same frequency Photon energy unaffected Interfere constructively with incoming waves (reflection) Phase lag (refraction) Wave crests of transmitted wave slowed relative to incident wave f = c λ f = v λ ' v = c n E = hf λ ' = λ c / v = λ n Geometric Optics Must include k in Maxwell s Equations when EM waves propagate in matter Þ Index of refraction, n If l much shorter than the objects with which it interacts Assume that light propagates in straight lines (s) Will focus on REFLECTION and REFRACTION of these s at the interface of two materials incident reflected Material 1 Material 2 refracted 4
l 1 Reflection Angle of incidence = angle of reflection q i =q r both angles are measured from the normal All s lie in the plane of incidence Why? When surface is a good conductor q i Electric field lines are perpendicular to the conductor surface q r The components of E parallel to the surface of the incident and reflected wave must cancel E ix = E cosθ i E rx = E cosθ r E ix + E rx = 0 θ i = θ r Refraction How is the angle of refraction related to the angle of incidence? q 1 cannot equal q 2 Why?? Remember v = fl ¹ Þ v 1 ¹ v 2 Frequencies (f 1,f 2 ) must be the same Þ wavelengths must be different q 2 must be different from q 1 q 1 q 2 l 2 λ 1 λ 2 = v 1 v 2 = 5
Snell s Law From the last slide: l 1 q 1 q 1 L q 1 q 2 q 2 q 2 l 2 q 2 The two triangles above each have hypotenuse L \ L = λ 2 sinθ 2 = λ 1 sinθ 1 λ 1 λ 2 = sinθ 1 sinθ 2 But, λ 1 λ 2 = v 1 v 2 = sinθ 1 = sinθ 2 DEMO Refraction 6
iclicker Which of the following diagrams could represent the passage of light from air through glass and back to air? (n air =1 and n glass =1.5) (a) (b) (c) Glass Glass Glass Dispersion n is a function of l How a prism works Exit face has a differently directed normal Blue light bends more sharply towards the first normal Then bends more sharply AWAY from the second normal. White Light Prism Split into Colors 7
Dispersion n(l) Taking into account n(l) is important in optical design of lenses, etc. Total Internal Reflection Consider light moving from glass ( =1.5) to air ( =1.0) sinθ 2 sinθ 1 = > 1 θ 2 > θ 1 Light bent away from the normal As q 1 gets bigger, q 2 gets bigger, but q 2 never bigger than 90 incident q 1 q r q 2 refracted reflected GLASS AIR 8
Total Internal Reflection sinθ 2 sinθ 1 = > 1 In general, if sin q 1 > ( / ), we have NO refracted Total internal reflection θ 2 > θ 1 incident q 1 q r q 2 refracted reflected GLASS AIR We define the critical angle such that sinq C =1 sinθ c = sin90 = Total Internal Reflection Increase incidence angle Reflected intensity increases, transmitted intensity decreases At q c, the transmission drops to ZERO TOTAL INTERNAL REFLECTION at the critical angle Also BEYOND the critical angle The transmitted wave skimming along the surface at q c actually has zero intensity The property of internal reflection is used for light fibers 9
DEMO Total Internal Reflection DEMO Light Pipes 10
DEMO Pouring Laser Light Relative Intensity of Reflected and Refracted Light Reflected intensity for normal incidence I = n n 1 2 + 2 I 0 For air and glass: = 1, = 1.5 2 I = 1 1.5 I 1+1.5 0 = 0.5 I 2.5 0 = 0.04I 0 2 4% of the light gets reflected, 96% goes through. 11