#### Transcript PHYSICS 2310

Phys 2310 Mon. Aug. 29, 2011 Today’s Topics – Properties of Light • Finish Detection of Light • Chapter 4: Propagation of Light – Homework Assigned • Reading for Next Time 1 Supplementary Material: Detection of Light • Detectors for Infrared Wavelengths – Similar to CCDs at l < 25 mm – Largest formats are 2K x 2K • High Cost ( ~ $500K) – Use at l > 3 mm requires liquid He cooling (4 oK) – Longer wavelength detectors (l > 25 mm ) require use of bolometers • Electrical resistance depends on temperature below 4 oK – Measurement of minute temperature changes due to photon absorbtion 2 Supplementary Material: Detection of Light • Detectors for Microwave and Radio Wavelengths – Electric field in radio wave excites electrons in antenna • Amplification produces detectable signal – Modern electronics technology sufficiently fast to detect and amplify signals. – Both phase and amplitude of photons can be detected (why?) 3 Supplementary Material: Detection of Light • Detectors for Ultraviolet and X-ray Wavelengths – High energy of photons results in strong photoelectric effect • Electrons emitted from solids when photons absorbed 4 Supplementary Material: Signal Detection • Photon rate from a source (N) is never constant – Signal is an average rate over a given time interval – Can’t detect a fraction of a photon • Some time intervals contain little more or little less – Poisson (counting) statistics: sN = sqrt(N) – Signal is seldom (never) without some sort of background – Almost all detectors has some intrinsic noise – Uncertainty in any detection is the combination of all these effects – Any measurement has an associated uncertainty 5 Supplementary Material: Signal Detection • Uncertainty in any signal can be estimated – Without detailed information we assume any source of errors is distributed as a Gaussian distribution: x m 2 1 P( x) exp 2 2 s s 2 Uncertainty(s) can be estimated via a Gaussian fit to a histogram made from lots of individual measurements. Compute Mean, Standard Deviation. Alternatively just estimate. Errors from each source don’t add in same sense They are random and (usually) uncorrelated. So, add in quadrature: s T s 12 s 22 s 32 ... 6 Chapter 4: Propagation of Light • Photons interact with matter in a variety of ways – Photons encountering an opaque solid can be absorbed (black surface) or reflected (metal surface) – Photons encountering a transparent surface can be scattered if path length is long enough (no substance is perfectly transparent) – Enhanced scattering of bluer light in atmosphere makes sky blue • Molecules can be visualized as absorbing photons and then emitting them in a new direction (physics is complex) • Huygen’s Principle – Behavior of light can be understood as the scattering of “wavelets”. – A surface (real or imaginary) can be thought of as a number of scattering centers – Provides an explanation for the laws of reflection and refraction 7 Chapter 4: Huygen’s Principle • Huygen’s Principle: Propagation of light can be modeled as if scattering off atoms in such a way that the spherical “wavelets” constructively interfere to produce a wavefront. “Every point of a propagating wavefront serves as the source of spherical secondary wavelets, such that the wavefront at some later time is the envelope of these wavelets.” 8 Chapter 4: Properties of Optical Materials • We can define an equivalent optical path length by considering the index of refraction – If speed of light is slower in dense material the equivalent path in a vacuum would be longer. Hence: – O.P.L. = nd where n is the index of refraction and d is the material thickness • The concepts of optical path leads to Fermat’s Principle (see sec. 4.5 in text): “A light ray will take the path between two points that minimizes its travel time.” This is not strictly true but it is still a useful concept for deriving Snell’s Law (see below). 9 Chapter 4: Properties of Optical Materials • The optical path length is found to a function of wavelength – The index of refraction of most materials is higher at shorter wavelengths • Not strictly true over all wavelengths but applies over visible (more about this later) • Over broader wavelength this effect (dispersion) is readily seen 10 Chapter 4: Plane Surfaces • Light slows as it enters a transparent medium – Light path (ray) is deflected toward normal when entering higher index medium – Light path (ray) is deflected away from normal when entering lower index medium • Note that dispersion is occurs such that blue light (higher index) is deflected more and vice versa 11 Chapter 4: Fermat’s Principle and Snell’s Law Minimizing the time (optical path length) between points Q and Q’ yields Snell’s Law: OPL nd n' d d ( h 2 ( p x ) 2 )1 / 2 d ' ( h' 2 x 2 )1 / 2 t QA AQ' v1 V2 t (h 2 ( p x) 2 )1/ 2 (h'2 x 2 )1/ 2 v1 v2 substituting : n[ h ( p x) ] 2 2 1/ 2 n' ( h' x ]) 2 2 1/ 2 differentiating : d n/2 n' / 2 2 ( 2 p 2 x )( 1 ) 2x 0 dx [ h ( p x) 2 ]1 / 2 ( h' 2 x 2 )1 / 2 thus, px x n ' [ h 2 ( p x) 2 ]1 / 2 ( h' 2 x 2 )1 / 2 or n px x n' d d' and n n sin n' sin ' Similarly, the law of reflection can also be derived (homework) 12 Chapter 4: Fermat’s Principle continued • This approach works for a variable index of refraction in which case the OPL is now an integral over the path: s2 OPL n( s ) ds s1 The book discusses an application of this concept to mirages. Note, that by setting d/dx = 0 the OPL doesn’t strictly have to be a minimum it could also be a maximum. A modern description is that we require alternative paths to have significant differences in phase of the “wavelets”. Thus we might think of the atoms as scattering the photons and the path light takes is the one where constructive interference is maximized. See the discussion on page 109-110 of text. 13 Chapter 4: Total Internal Reflection The light path of rays is reversible. • Thus we can consider total internal reflection via refraction. • Note that for rays 1-4 all appears fine. Ray 5 is a problem. • When we consider the reversed path any rays with >c will not emerge from the higher index medium. For glass (n ~ 1.52) c ~ 42 deg. So 45-deg prisms can be used. Substituting = 90 deg, or sin = 1 into Snell’s Law gives: n sin c n' 14 Chapter 4: Plane Surfaces continued • Light traversing a parallel plate is deflected (e.g. a window) • The deflection angle can be calculated d l sin( ' ) d l (sin cos ' sin ' cos ) from ABC: l t cos ' sin cos ' sin ' cos d t cos ' cos ' since : n sin n' cos n d t sin sin cos ' n' sin ' or : n cos d t sin 1 n ' cos ' 15 Homework this Week (HW #1) Homework this week due Wed., Sept. 8: Chapter 3: #14, 20, 24 Chapter 4: #6, 8, 9, 15, 17 16 Reading this Week By Wednesday: Finish Ch. 3,4 (3.6, 4.1 – 4.5, 4.7) Propagation of Light Begin Ch. 5 (5.1 – 5.2) Thin lenses 17