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 11/14/16 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? ε 0 ε, µ 0 µ Generally increased by the presence of matter especially ε => 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 n medium c = 1 µ 0 ε 0 n ε ε 0 = κ >1 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 0 C) 1.33 crown glass 1.52 diamond 2.42 3
Geometric Optics Must include κ in Maxwell s Equations when EM waves propagate in matter Index of refraction, n If λ 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 Reflection Angle of incidence = angle of reflection θ i =θ r both angles are measured from the normal All s lie in the plane of incidence Why? When surface is a good conductor θ i Electric field lines are perpendicular to the conductor surface θ 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 4
Refraction How is the angle of refraction related to the angle of incidence? θ 1 cannot equal Why?? Remember v = fλ θ 1 v 1 v 2 Frequencies (f 1,f 2 ) must be the same wavelengths must be different! must be different from θ 1 λ 1 λ 2 λ 1 λ 2 = v 1 v 2 = Snell s Law From the last slide: λ 1 θ 1 θ 1 L θ 1 λ 2 The two triangles above each have hypotenuse L L = λ 2 sin = λ 1 sinθ 1 λ 1 λ 2 = sinθ 1 sin But, λ 1 λ 2 = v 1 v 2 = sinθ 1 = sin 5
DEMO Refraction 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 6
Dispersion Ultraviolet absorption bands Increase n as the wavelength is decreased (higher frequency) 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. Index of refraction 1.54 1.52 1.50 White Light n blue >n red Prism frequency Split into Colors ultraviolet absorption bands Dispersion n(λ) Taking into account n(λ) is important in optical design of lenses, etc. 7
Total Internal Reflection Consider light moving from glass ( =1.5) to air ( =1.0) sin sinθ 1 = >1 > θ 1 Light bent away from the normal As θ 1 gets bigger, gets bigger, but never bigger than 90 incident θ 1 θ r refracted reflected GLASS AIR Total Internal Reflection sin sinθ 1 = >1 In general, if sin θ 1 > ( / ), we have NO refracted Total internal reflection > θ 1 incident θ 1 θ r refracted reflected GLASS AIR We define the critical angle such that sinθ C =1 sinθ c = 8
Total Internal Reflection Increase incidence angle Reflected intensity increases, transmitted intensity decreases At θ 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 θ c actually has zero intensity The property of internal reflection is used for light fibers DEMO Total Internal Reflection 9
DEMO Light Pipes DEMO Pouring Laser Light 10
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