Physics II

1. Physics II Scattering, rectilinear propagation, and the Law of Reflection Title PageTitle Page

2. In a vacuum Transmission of e-m radiation through a vacuum. S = E x B / ?o Right hand rule for TEM Rectilinear propagation in a vacuum. Rectilinear Propagation in a vacuumRectilinear Propagation in a vacuum

3. Reminder Phase relationships Part of vibration cycle Incoherent radiation No fixed (in time) relationship of phases Intensities add Coherent radiation Fixed relationship in phases Electric fields add Irradiance proportional to square of electric field Constructive Interference Destructive Interference Quick ReviewQuick Review

4. Small particles in a tenuous gas Ground state scattering Positive and negative charge centers form an oscillating dipole of +, - charge Do not absorb photon though because not enough energy to excite electron from ground state Atom re-radiates because of accelerating charge Radiates with electric field half wavelength out of phase with incident electric field. Destructive interference with incident wave in forward direction Re-emitted photon has same frequency as incident one. Small particles � Rayleigh scattering.Small particles � Rayleigh scattering.

5. Scattering centers far apart in tenuous gas No fixed phase relationship so there is no interference in scattering transverse to original beam direction Light scattered out sideways. But scattering at each center is quite weak But in forward direction As incident wave passes, the scattered light is 180 out of phase with it Forward scattering light from all centers is in phase then with each other but out of phase with incident wave front. Constructive interference in forward direction. Scattering off to sides in tenuous gas because there is no fixed phase relationship off the beam direction.Scattering off to sides in tenuous gas because there is no fixed phase relationship off the beam direction.

6. The symmetry principle involved. The direction of the original beam defines a unique direction for constructive interference so there is a strong forward scattering. The asymmetry introduced by the beam itself assures that all the scattered wavelets add constructively in the forward direction. Constructive interference in forward directionConstructive interference in forward direction

7. Rayleigh Scattering Rayleigh scattering Atoms have �resonant frequencies� as do all vibrating systems When excited close to resonance frequency the vibrations are especially strong. For tiny particles, the scattering is proportional to the fourth power of the frequency. Gave first clue that atmosphere was made up of particles small compared to wavelength of light. Rayleigh Scattering.Rayleigh Scattering.

8. Example A beam of white light crosses a large volume occupied by a tenuous molecular gas mixture of mostly oxygen and nitrogen. Compare the amount of scattering occurring fro the yellow (580nm) component with that of the violet (400nm) component. ExampleExample

9. Example Solution Problem statement (molecules) suggests apply ideas of Rayleigh scattering. Assume roughly equal number of oxygen and nitrogen scatterers. Amt yellow/amt violet =fy4 / fv4 =(?v/ ?y)4 Amt yellow/amt violet = (400/580)4 22.6 % Only about 1/5 as much yellow is scattered as violet. Solution to scattering exampleSolution to scattering example

10. Scattering in denser materials For example consider atmosphere at lower altitudes, say at STP How many molecules in a cube of edge comparable to wavelength of visible light? PV=nRT=NkBT (ideal gas law) N/V = P/(kBT) =1.01325x105 / (1.381x10-23 x 273.15) particles/m3 = 2.7 x 1025 particles per cubic meter. If ?=500 nm, ?3 =125 x 106 x10-27 =1.25x10-19m3 . N = 2.7 x 1.25 x 106 particles =3.4 x 106 particles Dav = (?3 / N)1/3 = 3.3 nm About 3 million molecules in a cube the size of the wavelength of visible light.About 3 million molecules in a cube the size of the wavelength of visible light.

11. Destructive interference almost everywhere except forward With a wavelength of 500 nm incident on more than 3 million particles about 3.3 nm apart, we cannot ignore the coherence of the scattered waves. Suppose a molecule scatters in some direction A molecule about half a wavelength away will also radiate and the two E-fields will cancel It is likely that there will always be pairs of molecules that have canceling radiation. The more dense, uniform, and ordered the medium the more complete the destructive interference and the less scattering in all but the forward direction! Forward scattering is coherent�beam moves straight on. Destructive interference in all but the forward direction.Destructive interference in all but the forward direction.

12. Remarks On molecule by molecule basis scattering is very weak. Molecule per molecule liquids scatter much less than gases. Transparent amorphous solids scatter only very weakly. Scattered remarksScattered remarks

13. Reflection Reflection is a result of scattering. Atomic separations on the order of 10-10 meters (X-Ray diffraction result) Wavelengths of visible light 1000 or so times larger than interatomic separation Unlike previous case, the discontinuity at reflecting surface allows backward scattering (in some directions) Reflection is a scattering phenomenon + discontinuities.Reflection is a scattering phenomenon + discontinuities.

14. Internal and External Reflections In practice it is the atoms within about � wavelength depth of interface that do the reflecting For normal incidence from air to glass, about 4 % of light is reflected ((1.5 -1)(1.5+1))2 Light incident from less to more optically dense medium is External reflection 180 degree relative phase shift in Electric field Light incident from more to less optically dense medium is Internal Reflection No relative phase shift Internal and External Reflections with concomitant phase shifts.Internal and External Reflections with concomitant phase shifts.

15. Some definitions redux A ray is a line drawn in space corresponding to the direction of flow of radiant energy (i.e., parallel to the Poynting vector) A wave front is a locus of points in a wave that have the same phase Wave fronts are surfaces to which the rays are perpendicular. Rays and wave fronts. Rays and wave fronts.

16. Huygen�s Principle Each point on a wave front serves as a source of secondary spherical wavelets, often considered modulated by the term (1 + cos(?) ) with ? the original ray direction. Huygens� PrincipleHuygens� Principle

17. Law of Reflection from Huygens Huygens� Construction for Reflection Law of Reflection � Huygens� GeometryLaw of Reflection � Huygens� Geometry

18. Proof 1 CD is the reflection of AB Wavelet emitted from A will reach C in phase with wavelet emitted from D. That is, if AC = BD Consider triangles ABD and ACD But BD = AD sin (?i) and AC = AD sin (?t) So sin (?i) = sin (?t) ?I = ?t Angle of incidence = angle of reflection Proof page 1Proof page 1

19. Law of reflection. The angle of incidence equals the angle of reflection. The angle made by the wavefront with the interface equals the angle made by the ray with the normal to the interface. The incident ray, the reflected ray, and the normal at the point of reflection all lie in the same plane. Law of reflection has two parts.Law of reflection has two parts.

20. Types of reflection Specular (as from a mirror) Diffuse (as from a rough surface) Real reflections lie somewhere between the above two extremes Types of reflectionTypes of reflection

21. Plane mirror Forms a virtual image Light rays do not pass through the image. Image Reverted (left to right) but not inverted (top to bottom) Image appears same distance behind mirror as object is in front of mirror. Plane mirror image properties.Plane mirror image properties.