Nature: Real (Converging Rays) Or Virtual (Diverging Rays)

Physics B AP Review: Optics, Modern, Waves Name:______

Naming optical images Explain your reasoning: Nature: real (converging rays) or virtual (diverging rays) Orientation: upright or inverted Size: true, enlarged or reduced

Law of Reflection Angle of incidence equals angle of reflection.

i = r

Plane Mirror Produces virtual, upright, and true sized images.

+ side - side of mirror of mirror Spherical Concave (Converging) Mirror f = ½ R Image is real when object is outside focus Image is virtual when object is inside focus

shiny dark Parts of spherical concave mirror. side side Shiny side 1. Plane Mirror (A-182 31) Principle Center of Focus axis Curvatur e + side - side Ray tracing: concave mirror Use two of the three principle rays: p-ray: parallel axis ray. f-ray: focus ray. c-ray: center ray.

An object is placed near a plane mirror, as shown Real image: Principle rays converge and image above. Which of the labeled points is the is constructed where they intersect as shown position of the image? below (use only two of the three shown) (A) A (B) B (C) C (D) D (E) E Explain your reasoning: c Real (should include ray tracing) Inverted Reduced object image

f image p

Virtual image: Principle rays diverge and image is constructed where the extension of the 2. Plane Mirror (A187 50) reflected rays intersect as shown below:

An object, slanted at an angle of 45, is placed in object image front of a vertical plane mirror, as shown above. c Virtual Which of the following shows the apparent Upright p position and orientation of the object's image? Enlarged image

4/29/2018 1 Bertrand Mirror and lens equation #1 Ray tracing: convex mirror 1/si + 1/so = 1/f Construction of image is best done using : si: image distance, +real, -virtual p-ray: parallel axis ray. so: object distance, +always c-ray: center ray. f: focal length, +converging, -diverging Virtual image: Principle rays diverge and image is Mirror and lens equation #2 constructed where the extension of the reflected M = -si/so = hi/ho rays intersect, as shown below: s : image distance, +real, -virtual i Virtual so: object distance, +always c p Upright hi: image height, -inverted, +upright Reduced ho: object height, +always image M: magnification >1 enlarged, <1 reduced, 1 true-sized

Spherical Convex (Diverging) Mirror f = ½ R Refraction Image is always virtual, upright, and reduced Light moves from one medium into another, changing speed when it refracts. Parts of spherical convex mirror. Light bends toward the normal when the first Shiny side medium has a lower refractive index than the second medium, and away from the normal Principle when the first medium has a higher refractive axis Focus Center of index than the second medium. Light doesn’t bend when refractive indices are equal. + side - side Curvature n Bending 1 toward the  normal 3. Concave mirror (A173 37) 1  2 n < n n 1 2 2 n 1 Bending away  1 from the  normal An object is placed as shown in the figure above. 2 n > n n 1 2 The center of curvature C and the focal point F 2 of the reflecting surface are marked. As compared with the object, the image formed by the reflecting surface is (A) erect and larger (B) erect and the same size (C) erect and smaller (D) inverted and larger (E) inverted and smaller Explain your reasoning by doing a ray tracing on the figure above!

4/29/2018 2 Bertrand 5. Refraction (A177 55) n No bending; 1 comes in on normal

Light leaves a source at X and travels to Y along the n 2 path shown above. Which of the following statements is correct? Index of Refraction (A) The index of refraction is the same for the two media. n = c/v (B) Light travels faster in medium 2 than in medium 1. (C) Snell's law breaks down at the interface. Snell’s Law (D) Light would arrive at Y in less time by taking a straight line path from X to Y than it n1sin(1) = n2sin(2) does taking the path shown above. (E) Light leaving a source at Y and traveling to X would 4. follow the same path shown above, but in reverse. Explain your reasoning:

6. Refraction (A276 31)

A light ray passes through substances 1, 2, and 3, as shown above. The indices of refraction for these three substances are n1, n2, and n3, respectively. Ray segments in 1 and in 3 are parallel. From the directions of the ray, one can conclude that (A) n3 must be the same as n1 (B) n2 must be less than n1 (C) n2 must be less than n3 (D) n1 must be equal to 1.00 (E) all three indices must be the same Explain your reasoning:

7. Refraction (A276 42)

4/29/2018 3 Bertrand A beam of white light is incident on a triangular glass prism with an index of refraction of about Real image: Principle rays converge and image is 1.5 for visible light, producing a spectrum. constructed where they intersect as shown below Initially, the prism is in a glass aquarium filled with air, as shown above. If the aquarium is filled with water with an index of refraction of image 1.3, which of the following is true? object f (A) No spectrum is produced. (B) A spectrum is produced, but the deviation of the p c beam is opposite to that in air. (C) The positions of red and violet are reversed in the Virtual image: Principle rays diverge and image spectrum. (D) The spectrum produced has greater separation is constructed where the extension of the between red and violet than that produced in air. reflected rays intersect, as shown below: (E) The spectrum produced has less separation between red and violet than that produced in air. Explain your reasoning: Virtual Upright Enlarged

image object p Total internal reflection Can occur when light is trying to leave a medium c into one with a smaller refractive index. The light bends away from the normal so 8. Converging Lens (A182 26) much it can’t get out of the material, and reflects inside the material instead.

Critical Angle of Incidence The smallest angle at which total internal reflection can occur. Which three of the glass lenses above, when n1sin(1) = n2sin(2) placed in air, will cause parallel rays of light to o n1sin(90 ) = n2sin(2) converge? n1 = n2sin(c) (A) I, II, and III (B) I, III, and V (C) l, IV, and V (D) II, III, and IV Converging Lens (E) II, IV, and V Thicker in the middle than on the edges Explain your reasoning: f (focal length) is a positive number Image is real when object is outside focus. Image is virtual, enlarged and upright when object is inside focus 9. Converging Lens (A182 69) Parts of a converging lens. If the object distance for a converging thin lens is more than twice the focal length of the lens, - side + side the image is Principle (A) virtual and erect (B) larger than the object axis f c f 2f 2f (C) located inside the focal point (D) located at a distance between f and 2f from Ray tracing with converging lens the lens Construction of image using two of the three (E) located at a distance more than by from the lens principle rays: Show your work: p-ray: parallel axis ray. (try using the lens equations) f-ray: focus ray. c-ray: center ray.

4/29/2018 4 Bertrand Ray tracing with diverging lens 10. Converging Lens (A276 30) Construction of image is best done using these two principle rays: p-ray: parallel axis ray. c-ray: center ray.

Virtual image construction: Principle rays always An object is placed at a distance of 1.5 from a diverge for this lens, and image is constructed where the extension of the reflected rays intersect converging lens of focal length , as shown as shown below: above. What type of image is formed and what is its size relative to the object? Type Size p (A) Virtual Larger Virtual (B) Virtual Same size object Upright Reduced image (C) Virtual Smaller always produced (D) Real Larger image (E) Real Smaller c Show your work: a) Do ray diagram on figure above b) Do calculation below 11. Diverging lens (S195 69) An illuminated object is placed 0.30 meter from a lens whose focal length is -0.15. meter. The image is (A) inverted, real, and 0,30 meter from the lens on the opposite side from the object (B) upright, virtual, and 0.30 meter from the lens on Converging Lens (A277 33) the opposite side, from the object A postage stamp is placed 30 centimeters to the (C) upright, real, and 0110 meter from the lens left of a converging lens of focal length 60 on the same side as the object centimeters. Where is the image of the stamp (D) upright, virtual, and 0. 10 meter from the located? lens on the same side as the object (A) 60 cm to the left of the lens (E) inverted, real, and 0. 10 meter from the lens (B) 20 cm to the left of the lens on the same side as the object (C) 20 cm to the right of the lens Show your work: (D) 30 cm to the right of the lens (E) 60 cm to the right of the lens Show your work:

12. General Lenses (S195 38) When one uses a magnifying glass to read fine print, one uses a (A) converging lens to produce a virtual image of the print Diverging Lens (B) converging lens to produce a real image of Thinner in the middle than on the edges the print f (focal length) is a negative number (C) mirror to produce a virtual image of the print Image is always virtual, upright, reduced (D) diverging lens to produce a real image of the print Parts of a converging lens. (E) diverging lens to produce a virtual image of the print Explain your reasoning: - side + side Principle axis 2f f c f 2f

4/29/2018 5 Bertrand 13. General Optics (S199 31) hf = Kmax +  or Kmax = hf -  The image of the arrow is larger than the arrow 15. Photoelectric Effect (A187 55) itself in which of the following cases? In an experiment, light of a particular wavelength is incident on a metal surface, and

electrons are emitted from the surface as a result, To produce more electrons per unit time but with less kinetic energy per electron, the experimenter should do which of the following? (A) Increase the intensity and decrease the wavelength of (A) I only (B) II only the light. (C) I and III only (D) II and III only (B) Increase the intensity and the wavelength of the light. (E) I, II, and III (C) Decrease the intensity and the wavelength of the light. (D) Decrease the intensity and increase the wavelength of Show your work or explain your reasoning the light. (E) None of the above would produce the desired result. Explain your reasoning or show work:

Light is a wave Absorption Spectrum c = f (speed is wavelength times frequency) Photon is absorbed and excites atom to higher energy state. Light is a particle Absorption indicated by upward arrows on A “particle” of light is called a photon energy-level diagrams. This is a “quantum” of light energy (quantum Creates dark bands, since the light disappears means smallest indivisible quantity) and goes into the atom.

Energy of a photon Emission Spectrum E = hf Photon is emitted and atom drops to lower energy state. 14. Photon Energy (A276 37) Emission indicated by downward arrows on If photons of light of wavelength  have energy energy-level diagrams. E, photons of wavelength 2 will have an energy Creates bright bands of color, since the light is of emitted and goes into the atom.

(A) 2E (B) E (C) ½ E Energy Level diagram (D) ¼ E (E) None of the above Horizontal lines indicate allowed atomic energies.

Show your work Atom cannot exist at “in between” energies. Upward arrows are absorptions Downward arrows are emissions Photon energies are calculated by examining the The “electron-volt” (eV) diagram An energy unit useful on the atomic level. Photon frequencies are calculated from Planck’s If a moving electron or proton is stopped by 1 equation Volt of electric potential, we say it has 1 electron-volt (or 1 eV) of kinetic energy! Ionization band 0 ev 1 eV = 1.60210-19 J -0.5 ev -2.5 ev 4.5 eV emission Photoelectric Effect experiment -4.3 ev Ephoton = Kmax +  -5 ev Ephoton = hf (Planck’s equation) Kmax: maximum kinetic energy of electrons 7.5 eV absorption (equal to stopping potential times charge of electron) : binding energy or “work function” -10 ev

4/29/2018 6 Bertrand ground state Fission: Heavy nucleus splits. 16. Atomic Fusion: Small nuclei combine. Spectra (A182 34) 17.

A hypothetical atom has four energy states as shown above. a) Which of the following photon energies could NOT be found in the emission spectra of this atom after it has been excited to the n = 4 state? (A) l eV (B) 2 eV (C) 3 eV (D) 4 eV (E) 5 eV Show your work or explain your reasoning

b) Which of the following transitions will produce the photon with the longest wavelength? (A) n = 2 to n = l (B) n = 3 to n = l (C) n = 3 to n = 2 (D) n = 4 to n = l (E) n = 4 to n = 3 Show your work or explain your reasoning

Nuclear Reactions Energy released an element changes from one to another. Lots of energy is released due to mass being destroyed. E = mc2 Mass + energy is conserved. Charge is conserved.

Nucleons Proton: Charge: +e; Neutron: Charge: 0

Nuclear reactions Nuclear Decay Alpha decay: He2+ released from nucleus Beta decay Beta Minus: e- released from nucleus Positron: e+ released from nucleus

4/29/2018 7 Bertrand 18. Nuclear Reactions (A355 45) b) Which of the following statements is always A proton collides with a nucleus of 14 N. If this true for neutron-induced fission reactions 7 235 11 involving U ? collision produces a nucleus of 6 C and one 92 other particle, that particle is I. The end products always include Ba and Kr. (A) a proton (B) a neutron II. The rest mass of the end products is less than (C) a deuteron (D) an  particle 235 1 that of U + n. (E) a  particle 92 0 Explain your reasoning or show your work: III The total number of nucleons (protons plus neutrons) in the end products is less than that 235 1 in U + n. 92 0 (A) lI only (B) Ill only (C) I and ll only (D) I and lll only (E) l,ll, and lll Explain your reasoning:

19. Nuclear Reactions (A355 34) The nuc1ear reaction X  Y + Z occurs spontaneously. If Mx, My, and Mz are the masses of the three particles, which of the following relationships is true?

(A) Mx < My - Mz (B) Mx < My + Mz (C) Mx > My + Mz (D) Mx - My < Mz 21. Nuclear Reactions (A098 12) (E) Mx - Mz < My Quantities that are conserved in all nuclear Explain your reasoning: reactions include which of the following? I. Electric charge II. Number of nuclei III. Number of protons (A) I only (B) II only (C) I and III only (D) II and III only (D) I, II, and III Explain your reasoning: 20. Nuclear Reactions (A093 32) Questions 32 - 33 deal with nuclear fission for which the following reaction is a good example. 235 1 138 95 U + n  Ba + Kr + neutrons + enrgy 22. Nuclear Reactions (A187 33) 92 56 0 36 A negative beta particle and a gamma ray are emitted during the radioactive decay of a nucleus a) The total number of free neutrons in the of 214 . Which of the following is the products of this reaction is 82 Pb (A) 2 (B) 3 (C) 4 (D) 5 (E) 6 resulting nucleus? Show your work: 214 214 213 (A) 80 Hg (B) 81 Tl (C) 83 Bi

214 218 (D) 83 Bi (E) 84 Po

Show your work:

4/29/2018 8 Bertrand Wave-Particle Duality Waves are particles and particles are waves 26. Wave-particle duality (A266 35) Energy Which of the following graphs best represents Particle: E = K + U the de Broglie wavelength  of a particle as a Photon: E = hf function of the linear momentum p of the Momentum particle? Particle: p = mv Photon: p = h/ Wavelength Photon:  c/f Particle:  = h/p (deBroglie wavelength)

23. Wave-particle duality (A187 34) If the momentum of an electron doubles, its de Broglie wavelength is multiplied by a factor of

(A) ¼ (B) ½ (C) 1 (D) 2 (E) 4 Show your work:

Explain your reasoning:

24. Wave-particle duality (A271 37) Of the following phenomena, which provides the 27. Photon Momentum (A276 37) best evidence that light can have particle If photons of light of frequency  have properties? momentum p, photons of light of frequency 2 (A) Interference of light in thin films will have a momentum of (B) Electromagnetic radiation (A) 2 p (B) 2 p (C) p (C) Photoelectric effect p 1 (D) Electron diffraction p (E) X-ray diffraction (D) 2 (E) 2 Explain your reasoning: Show your work

25. Wave-particle duality (A271 38) Of the following phenomena, which provides the best evidence that particles can have wave properties? (A) The absorption of photons by electrons in an atom Compton Scattering (B) The a-decay of radioactive nuclei Proof of the momentum of photons. (C) The interference pattern produced by neutrons High-energy photons collided with electrons. incident on a crystal Conservation of momentum. (D) The production of x-rays by electrons striking a Scattered photons examined to determine loss of metal target (E) The scattering of photons by electrons at rest momentum. Explain your reasoning: Davisson-Germer Experiement Verified that electrons have wave properties by proving that they diffract.

4/29/2018 9 Bertrand Shone electrons onto a metal strip; they 30. diffracted like light to form a diffraction pattern. Rutherford Scattering Collided alpha particles onto a gold foil strip. Unexpectedly large back-scattering indicated elastic collision of the alpha particles with nuclei in the atoms. Evidence of a nuclear atom with a dense positive nucleus.

Milliken Oil Drop Experiment Suspended charged oil drops in electric field. Proved that the charge on an electron was the smallest possible charge (or quantum of charge).

Photoelectric effect Showed that the energy of photons depended upon the frequency of incident light, and not on its intensity. Showed that Planck’s equation E = hf was correct. Evidence of the particle nature of light. Won Einstein his Nobel Prize.

28. Classic Experiments (A187 11) Which of the following experiments provided evidence that electrons exhibit wave properties? I. Millikan oil-drop experiment II. Davisson-Germer electron-diffraction experiment III. J. J. Thomson's measurement of the charge-to-mass ratio of electrons (A) I only (B) II only (C) I and III only (D) II and III only (E) I, II, and III Explain your reasoning:

29. Classic Experiments (A187 35) Quantum concepts are critical in explaining all of the following EXCEPT (A) Rutherford's scattering experiments (B) Bohr's theory of the hydrogen atom (C) Compton scattering (D) the blackbody spectrum (E) the photoelectric effect Explain your reasoning:

4/29/2018 10 Bertrand 31. Classic Experiments (A444 46) Wave types The scattering of alpha particles by a thin gold A transverse wave: particles of the medium foil was measured by Geiger and Marsden. The oscillate perpendicular to direction of wave Rutherford model of the atom was proposed in propagation. Example: waves on a string order to explain why A longitudinal wave (also called a compression (A) more particles were scattered through angles wave): particles of the medium oscillate greater than 90° than were scattered through parallel to direction of wave propagation. angles less than 90° Example: sound (B) the fraction of particles scattered through large angles was too large to be explained by previous models of the atom Light (C) no particles passed through the foil undeflected A transverse electromagnetic wave that (D) the most common scattering angle was about 90° requires no medium through which to travel. (E) the most common scattering angle was about l80° Explain your reasoning: 33. Wavelength and frequency (A182 52) A radar operates at a wavelength of 3 centimeters. The frequency of these waves is (A) 10-10 Hz (B) 106 Hz (C) 108 Hz (D) 3 x 108 Hz (E) 1010 Hz Show your work: 32. Wave Particle Duality (A444 64) Which of the following statements is true of a beta particle? (A) Its speed in a vacuum is 3 x 108 m/s. (B) It has a charge equal and opposite to that of an alpha particle. (C) It is more penetrating than a gamma ray of the same energy. Reflection of waves (D) It has a mass of about 1,840 times that of a proton. (E) It can exhibit wave properties. A wave strikes a medium boundary and Explain your reasoning “bounces back” into original medium. Fixed-end reflection: inverted phase. Occurs when reflecting medium has greater density. Open-end reflection: Same phase. Occurs when reflecting medium has lesser density.

34. Reflection of Waves (A187 29)

Mechanical Wave A disturbance that propagates through a medium with little or no net displacement of the particles of the medium. One end of a horizontal string is fixed to a wall. Parts of a Wave A transverse wave pulse is generated at the other Crest: high point; Trough: low point end, moves toward the wall as shown above, and Equilibrium: mid point is reflected at the wall. Properties of the reflected Amplitude: distance from equilibrium to crest or pulse include which of the following? trough I. It has a greater speed than that of the Wavelength: distance between adjacent crests incident pulse. II. It has a greater amplitude than that of the incident pulse. Speed of a wave III. It is on the opposite side of the string Distance traveled by a given point on the wave from the incident pulse. (such as a crest) in a given interval of time. (A) I only (B) III only (C) I and II only v = d/t and v = ƒ (D) II and III only (E) I, II, and III Explain your reasoning: Period of a wave T = 1/ƒ (reciprocal of frequency)

4/29/2018 11 Bertrand Refraction of waves 36. Superposition (A444 28) Transmission of wave from one medium to another. Refracted waves may change speed and wavelength. Refracted waves do not change frequency. Two wave pulses, each of wavelength , are 35. Refraction of Waves (A187 27) traveling toward each other along a rope as When light passes from air into water, the frequency shown above. When both pulses are in the region of the light remains the same. What happens to the between points X and Y. which are a distance  speed and the wavelength of light as it crosses the apart, the shape of the rope will be which of the boundary in going from air into water? following? Speed Wavelength Explain your reasoning: (A) Increases Remains the same (B) Remains the same Decreases (C) Remains the same Remains the same (D) Decreases Increases (E) Decreases Decreases Explain your reasoning:

37. Superposition (A182 59)

Principle of Superposition When two or more waves pass a particular point in a medium simultaneously, the resulting displacement at that point in the medium is the The figure above shows two wave pulses that are approaching each other. Which of the following sum of the displacements due to each individual wave. The waves interfere with each other. best shows the shape of the resultant pulse when the centers of the pulses, points P and Q. Types of interference. coincide? Explain your reasoning: If the waves are “in phase” (crests and troughs aligned) the amplitudes are summed. This is called constructive interference. If the waves are “out of phase” (crests and troughs are completely misaligned) the amplitudes are substracted. This is called destructive interference.

Sounds in the Real World Because of superposition and interference, real world waveforms may not appear to be pure sine or cosine functions. That is because most real 38. Wave on a string (A182 27) world sounds are composed of multiple frequencies.

Standing Wave A standing wave is a wave that is reflected back A standing wave of frequency 5 hertz is set up and forth between fixed ends (of a string or pipe, on a string 2 meters long with nodes at both ends for example). Reflection may be fixed or open- and in the center, as shown above. ended. Superposition of the wave upon itself a) The speed at which waves propagate on the results in constructive interference and an string is enhanced wave. (A) 0.4 m/s (B) 2.5 m/s (C) 5 m/s (D) 10 m/s (E) 20 m/s

4/29/2018 12 Bertrand Show your work: 40. Problem: Doppler Effect (A182 58) In the Doppler effect for sound waves, factors that affect the frequency that the observer hears include which of the following? I. The speed of the source II. The speed of the observer b) The fundamental frequency of vibration of III. The loudness of the sound the string is (A) I only (B) III only (C) I and II only (A) 1 Hz (B) 2.5 Hz (C) 5 Hz (D) II and III only (E) I, II, and III (D) 7.5 Hz (E) 10 Hz Explain your reasoning: Show your work:

Beats The characteristic loud-soft pattern that characterizes two nearly (but not exactly) 41. Doppler Effect (A276 49) matched frequencies.

39. Interference (A622 32)

A small vibrating object on the surface of a ripple tank is the source of waves of frequency Two sinusoidal functions of time are combined 20 Hz and speed 60 cm/s. If the source S is to obtain the result shown in the figure above. moving to the right, as shown above, with speed Which of the following can best be explained by 20 cm/s, at which of the labeled points will the using this figure? frequency measured by a stationary observer be (A) Beats (B) Doppler effect greatest? (C) Diffraction (D) Polarization (A) A (B) B (C) C (D) D (E) Simple harmonic motion (E) It will be the same at all four points. Explain your reasoning: Explain your reasoning:

Resonance Occurs when a vibration from one oscillator occurs at a natural frequency for another Diffraction oscillator. The first oscillator causes the second The bending of a wave around a barrier. to vibrate. Diffraction of light combined with interference of diffracted waves causes “diffraction patterns”. Doppler Effect The raising or lowering of perceived pitch of a Double-slit or multi-slit diffraction sound based on the relative motion of the observer and the source of the sound. When an n = d sin ambulance is racing toward you, the sound of its d: spacing between slits (m) siren appears to be higher in pitch. When the n: bright band numger ambulance is racing away from you, the sound of Note: Although it is most commonly applied to its siren appears to be lower in pitch. light, the diffraction equation also works for sound or other mechanical waves.

4/29/2018 13 Bertrand 42. Diffraction (A276 51)

Plane sound waves of wavelength 0.12 m are incident on two narrow slits in a box with nonreflecting walls, as shown above. At a distance of 5.0 m from the center of the slits, a first-order maximum occurs at point P, which is 3.0 m from the central maximum. The distance between the slits is most nearly (A) 0.07 m (B) 0.09 m (C) 0.16 m (D) 0.20 m (E) 0.24 m Show your work:

Single-slit diffraction These are less well defined patterns consisting of central bright spot surrounded by dark bands n = s sin; n: dark band number; s: slit width

43. Single-slit diffraction (A177 27) Which of the following is true of a single-slit diffraction pattern? (A) It has equally spaced fringes of equal intensity. (B) It has a relatively strong central maximum. (C) It can be produced only if the slit width is less than one wavelength. (D) It can be produced only if the slit width is exactly one wavelength. (E) It can be produced only if the slit width is an integral number of wavelengths. Explain your reasoning:

4/29/2018 14 Bertrand