n 1 sin 1 n 2 sin 2 Light and Modern Incident ray Normal 30.0 Air Glass Refracted ray speed of light in vacuum speed of light in a medium c v

Transcription

1 Light and Modern E hf n speed of light in vacm speed of light in a medim c v n sin n sin Incident ray Normal TIP. The reqency Remains the Same The freqency of a wave does not change as the wave passes from one medim to another. Both the wave speed and the wavelength do change, bt the freqency remains the same. n n Air Glass 30.0 n > n < Refracted ray White light R B Red (b) Ble

2 M image height object height h h h P p Q R q P h Object Image M h h q p Principal axis h O a C a I h V p q f q R p ront Back O I C p q

3 3 O C I Principal axis ront Back (a) 3 C O I ront Back (b) 3 O I C ront Back

4 O 3 ront Back I I O ront 3 Back (a) (b) 3 O I ront Back (c) Rays of light go throgh a lens. Mind yor p s and q s!

5 Spherical Aberration Chromatic Aberration Violet Red R igre 3.3 V Red Violet Chromatic aberra-

6 YOUNG S DOUBLE-SLIT EXPERIMENT max min max S min S 0 max S min irst screen Second screen Condition for constrctive interference (two slits) (a) C max min max Screen b, M. Cagnet, M. rancon, J. C. Thier (b) d sin bright m m 0,,,... d sin dark (m ) m 0,,,... [4.3] Condition for destrctive interference (two slits) y dark L d (m ) m 0,,,...

7 SINGLE-SLIT DIRACTION Incoming wave Lens Slit (a) f Screen (b) b, rom M. Cagnet, M. rancon, and J. C. Thierr, Atlas of sin dark m a m,, 3,... [4.] Condition for destrctive interference (single slit) THE DIRACTION GRATING Incoming plane wave of light P irst-order maximm (m = ) m 0 Central (or zeroth-order) maximm (m = 0) Diffraction grating P irst-order maximm (m = ) _ l _ l l l d d 0 d d sin ACTIVE IGURE 4.0 d sin bright m m 0,,,... d d d sin

8 INTERERENCE IN THIN ILMS 80 phase change No phase change 80 phase change Air Srface A ilm with index n Air n = 80 phase change t SiO n =.45 t Srface B Air Si n = 3.50 Problem-Solving Strategy Thin-ilm Interference The following steps are recommended in addressing thin-film interference problems:. Identify the thin film casing the interference, and the indices of refraction in the film and in the media on either side of it.. Determine the nmber of phase reversals: zero, one, or two. 3. Conslt the following table, which contains Eqations 4.9 and 4.0, and select the correct colmn for the problem in qestion: Eqation (m 0,,...) phase reversal 0 or phase reversals nt (m ) [4.9] constrctive destrctive nt m [4.0] destrctive constrctive 4. Sbstitte vales in the appropriate eqations, as selected in the previos step.

9 Photoelectrons C E Light KE max ev s V Variable power spply A oelectric effect ca K E max hf KE max c = f iλ f c f

10 to prodce constrctive interference when this path differenc atoms lie in eqally spaced planes. Now sppose an x-ray beam is incide 0.48 nm grazing angle on one of the planes, as in igre 7.3. The beam ca mltiple of the wavelength reflected. The from both condition the pper and lower plane for of atoms. constr However The Compton shift formla geometric constrction in igre 7.3 shows that the beam reflected given by x-ray beam of wavelength 0 toward a block of graphite. He fond that the scattered x-rays had a slightly longer wavelength than the incident x-rays, and hence the energies of the scattered rays were Answer lower. The amont of energy redction depended on the angle at which the x-rays were scattered. The change in wavelength between a scattered x-ray and an incident x-ray is called the Compton shift. In order to explain this effect, Compton assmed that if a photon behaves like a particle, its collision with other particles is similar to a collision between two billiard balls. Hence, the x-ray photon carries both measrable energy and momentm, and these two qantities mst be conserved in a collision. If the incident photon 7.5 THE COMPTON EECT given by d sin m (m,, 3,...) collides with an electron initially at rest, as in igre 7.6, the photon transfers some of its energy and momentm to the electron. As a conseqence, the energy and freqency of the scattered photon are lowered and its wavelength increases. Applying relativistic energy and momentm conservation to the collision described in igre 7.6, the shift in wavelength of the scattered photon is given by d sin m (m,, 3,...) rther X-rays jstification for the photon natre of light came from an experiment condcted by Arthr H. Compton in 93. In his experiment, Compton directed an Incident Reflected beam beam x-ray beam 0 h of wavelength [7.] m Crystal e c ( cos ) 0 toward a block of graphite. He fond that the scattered x-rays had a slightly Incident longer wavelength than the incident x-rays, Reflected and hence the energies of the scattered X-ray beam rays were lower. The amont of energy redction beam depended igre 7.3 tbe on the angle at which the x-rays were scattered. The change in wavelength ARTHUR HOLLY COMPTON, Upper plane American Physicist (89 96) d between a scattered Collimator Photographic x-ray and an incident x-ray is called the Compton shift. Compton was born in Wooster, Ohio, Lower andplane In order to explain film this effect, Compton assmed that if a photon behaves like a he attended Wooster College and Princeton d sin eqal to d sin. University. He became director of the laboratory at the University of Chicago, where particle, its collision with other particles is similar to a collision between two billiard balls. Hence, the x-ray photon tained chain reactions carries was condcted. both This measrable energy and momentm, experimental work concerned with ss- work was of central importance to the and these two qantities mst constrction be conserved of the first atomic bomb. His in a collision. If the incident photon discovery of the Compton effect and his collides with an electron initially work with at cosmic rest, rays led to his as sharing in the igre 7.6, the photon transfers 97 Nobel Prize in physics with Charles some of its energy and momentm Wilson. to the electron. As a conseqence, the energy Recoiling electron and Upper freqency planeof the scattered photon are lowered and its wavelength increases. φ Applying relativistic energy and momentm conservation to the collision described in igre 7.6, the shift in wavelength of the scattered θ f 0, λ 0 d photon is given by where m e is the mass of the electron and is the angle between the directions of the scattered and incident photons. The qantity h/m e c is called the Compton wavelength and has a vale of nm. The Compton wavelength is very small relative to the wavelengths of visible light, so the shift in wavelength wold be difficlt to detect if visible light were sed. rther, note that the Compton shift depends on the scattering angle and not on the wavelength. Experimental reslts for x-rays scattered from varios targets obey Eqation 7. and strongly spport the photon concept. Qick Qiz 7. An x-ray photon is scattered by an electron. The freqency of the scattered photon relative to that of the incident photon (a) increases, (b) decreases, or (c) remains the same. Lower plane f, λ λ Cortesy of AIP Niels Bohr Library igre 7.6 Diagram representing Compton scattering of a photon by an electron. The scattered photon has less energy (or a longer wavelength) than the incident photon. d sin the lower srface travels farther than the beam reflected from the pper s by a distance of d sin. The two portions of the reflected beam will com to prodce constrctive interference when this path difference eqals some int mltiple of the wavelength. The condition for constrctive interferen 0 h m e c ( cos ) [ A two-dimens depiction of the reflection of beam from two parallel crystal planes separated by a distance beam reflected from the lower travels farther than the one re from the pper plane by an am igre depiction beam fro planes se beam refl travels far from [7.] the eqal to where m e is the mass of the electron and is the angle between the directions of the scattered and incident photons. The qantity h/m e c is called the Compton wavelength and has a vale of nm. The Compton wavelength is very small

11 E hf hc p E c hc c h h p h mv f E h x p x E t h 4 h 4

12 ENERGY n Balmer series Lyman series ACTIVE IGURE 8.7 E (ev) Paschen series E n 3.6 n ev R H n f n i Three Qantm Nmbers for the Hydrogen Atom Nmber of Qantm Allowed Nmber Name Allowed Vales States N Principal qantm nmber,, 3,... Any nmber Orbital qantm nmber 0,,,..., n n m Orbital magnetic qantm,,..., nmber 0,...,,

13 Atom in grond state E Atom in excited state E E 4 E 3 hf E E E E Before After E igre 8.6 Energy level diagram Atom in excited state Atom in grond state Atom in excited state Atom in grond state E E E E hf E hf = E hf = E E hf E E E E Before After Before After

14 E = mc N(t) N 0 N =N 0 e t N 0 4 N 0 T / T / t R N t ACTIVE IGURE 9.6 N N N 0 e t T / ln 0.693