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_{PH203KUZMASPRING2014}
This is a separate 1-credit course that requires registering with the registrar's office
Course # | Section | Day, Time | Place | Workshop leader | ||
---|---|---|---|---|---|---|
PH 299-001 | 62985 | Th | 12:00-13:15 | NH 385 | Ameena Alattar | aka6 |
PH 299-003 | 62982 | Th | 14:00-15:50 | NH 391 | Bee Bui | bui |
PH 299-002 | 62980 | Fr | 10:15-12:05 | NH 389 | Patrick Bradley | pat5 |
PH 299-006 | 62983 | Fr | 14:00-15:50 | CH 254 | Eliza Slater | elizaslater @ gmail |
ph299_syllabus_14sp.pdf: available for download as a PDF file
A photon of wavelength $2.0\times 10^{-11}\,$m strikes a free electron of mass $m_e$ that is initially at rest. After the collision, the photon is shifted in wavelength by an amount $\;\Delta\lambda=\frac{2h}{m_ec}\,$, and reversed in direction.
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A photon of energy 240 keV is scattered by a free electron. If the recoil electron has a kinetic energy of 190 keV, what is the wavelength of the scattered photon?
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An incident photon of wavelength 0.0100 nm is Compton scattered; the scattered photon has a wavelength of 0.0124 nm. What is the change in kinetic energy of the electron that scattered the photon?
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Two different monochromatic light sources, one yellow (580 nm) and one violet (425 nm), are used in a photoelectric effect experiment. The metal surface has a photoelectric threshold frequency of $6.20\times 10^{14}\,$Hz.
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What are the de Broglie wavelengths of electrons with the following values of kinetic energy?
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What is the ratio of the wavelength of a 0.100-keV photon to the wavelength of a 0.100-keV electron?
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What is the de Broglie wavelength of a basketball of mass 0.50 kg when it is moving at 10 m/s? Why don't we see diffraction effects when a basketball passes through the circular aperture of the hoop?
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An electron passes through a slit of width $1.0\times 10^{-8}\,$m. What is the uncertainty in the electron’s momentum component in the direction parallel to the slit?
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If the momentum of the basketball (see problem above) has a fractional uncertainty of $\frac{\Delta p}{p} = 10^{-6}$, what is the uncertainty in its position?
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Halogen light bulbs can have higher filament temperatures than regular incandescent bulbs. A standard light bulb operates at about 2900 K while a halogen bulbs might be 3500 K hot.
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A spaceship moves at a constant velocity of $0.40c$ relative to an Earth observer. The pilot of the spaceship is holding a rod, which he measures to be 1.0 m long.
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A rectangular plate of glass, measured at rest, has sides 30.0 cm and 60.0 cm.
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A spaceship travels at constant velocity from Earth to a point 510 ly away as measured in Earth's rest frame. The ship's speed relative to Earth is $0.99c$. A passenger is 20 yr old when departing from Earth in the year 2000.
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Electron A is moving west with speed $0.6c$ relative to the lab. Electron B is also moving west with speed $0.8c$ relative to the lab. What is the speed of electron B in a frame of reference which electron A is at rest?
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An observer on earth notices two spaceships approach at speeds of $0.75c$ and $0.5c$ respectively. What is the relative speed between the spaceships as measured by a passenger of one of the spaceships?
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A constant force is applied to a particle initially at rest. Sketch qualitative graphs of the particle's speed, momentum, and acceleration as functions of time. Assume that the force acts long enough so the particle achieves relativistic speeds.
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An electron is accelerated from rest through a potential difference of $1 \times 10^7\,$V (also consider $1 \times 10^8\,$V).
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Why is it harder to accelerate a proton to a speed close to the speed of light, than is to accelerate an electron to the same speed?
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A nuclear power plant generates $10\times 10^9\,$W of power. Assuming 100% efficiency, by how much does the mass of the fuel change in one day to produce this much energy?
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Find the radii to which the sun and the earth must be compressed for them to become black holes.
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The interference pattern shown in the figure below is produced by light with a wavelength of 450 nm passing through two slits with a separation of 50 $\mu$m. After passing through the slits, the light forms a pattern of bright and dark spots on a screen located 1.25 m from the slits. What is the distance between the two vertical, dashed lines in the figure below?
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In a single-slit diffraction experiment, the width of the slit is 1.90 $\mu$m. If a beam of light of wavelength 632 nm forms a diffraction pattern,
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Why can you easily hear sound around a corner, while you cannot see around the same corner?
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If diffraction were the only limitation, what would be the maximum distance at which the headlights of a car could be resolved (seen as two separate sources) by the naked human eye? – The diameter of the pupil of the eye is about 7 mm when dark-adapted. Make reasonable estimates for the distance between the headlights and for the wavelength.
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The Hubble space telescope has an aperture with a diameter of 2.4 m. How close together can two asteroids at $5\times 10^{10}\,$m distance be if they are still seen as two objects (assume $\lambda=500\,$nm)?
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A film of soapy water in air is held vertically and viewed in reflected light. The film has index of refraction $n = 1.36$.
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A sodium light ($\lambda = 589.3\,$nm) is used to view a soap film to make it look black when directed perpendicular to the film. What is the minimum thickness of the soap film if the index of refraction of soap solution is 1.36?
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A nonreflective coating of magnesium fluoride ($n=1.38$) is applied to a camera lens ($n=1.5$). If one wants to prevent light at a wavelength of 560 nm to reflect from the lens, what minimum thickness does the coating need to be?
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The figure shows two rays of light encountering interfaces, where they reflect and refract. Which of the resulting waves are shifted in phase at the interface?
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A diffraction grading produces a bright fringe at an angle of 14$^\circ$ for 400 nm. For another wavelength the same order (m) fringe is at an angle of 27$^\circ$.
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A diverging lens ($f=-5\,$cm) is located 25 cm to the right of a converging lens ($f=10\,$cm). A beetle (length = 2 cm) is 30 cm to the left of the converging lens.
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The near point of a farsighted person is 65 cm. What power contact lens he must use to correct this problem and be able to read a book at a normal near point of 25 cm?
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A stamp $1.5\,{\text{cm}}\times 2\,{\text{cm}}$ is viewed through a magnifying glass with $f=10\,$cm. What is the size of the stamp if the observer’s eye is relaxed and has a near point distance of 25 cm?
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Jenna is farsighted; the nearest object she can see clearly without corrective lenses is 2.0 m away. It is 1.8 cm from the lens of her eye to the retina.
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A nearsighted woman cannot clearly see objects more than 2.0 m away. The distance from the lens of the eye to the retina is 1.8 cm, and the eye's power of accommodation is 4.0 D (the inverse focal length of the cornea-lens system increases by a maximum of 4.0 dpt over its relaxed inverse focal length when accommodating for nearby objects). Assume the corrective lenses are 2 cm from the eyes.
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A telescope of an amateur astronomer has an angular magnification of $–200$. The eyepiece has a focal length of 5 mm.
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In a microscope, the objective lens has a short focal length, whereas in a telescope, the objective lens has a long focal length. Explain the reason for the difference in focal lengths.
A photographer wishes to take a photo of the Eiffel Tower (300 m tall) from across the Seine River, a distance of 500 m from the tower. What focal length lens should she use to get an image that is 20 mm high on the film?
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Location | Orientation | Size | Real/Virtual |
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Beyond 2F | inverted | reduced | real |
At 2F | inverted | same | real |
Between F and 2F | inverted | enlarged | real |
Just Beyond F | inverted | approaching infinity | real |
Just Inside F | upright | approaching infinity | virtual |
Between F & Lens | upright | enlarged | virtual |
Location | Orientation | Size | Real/Virtual |
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Anywhere | upright | reduced | virtual |
A fish hovers beneath the still surface of a pond. If the sun is 33$^\circ$ above the horizon, at what angle above the horizontal does the fish see the sun? ($n_\text{water} =1.33$)
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The sunlight reflected from the surface of a lake is completely polarized. Calculate the angle of incidence of the sunlight
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A beam of light strikes one face of a window pane with an angle of incidence of 30.0$^\circ$. The index of refraction of the glass is 1.52. The beam travels through the glass and emerges from a parallel face on the opposite side. Ignore reflections.
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In an experiment a beam of red light of wavelength 645 nm in air passes from glass into air. The incident and refracted angles are $\theta_1$ and $\theta_2$, respectively. In the experiment, angle $\theta_2$ is measured for various angles of incidence, and the sine's of the angles are used to obtain the line shown in the following graph.
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The plano-convex lens shown to the right has a focal length of 20 cm in air. An object is placed 60 cm ($3f$) from this lens.
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A thin converging lens of focal length 8 cm is used as a simple magnifier to examine an object $K$ that is 6 cm from the lens.
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Location | Orientation | Size | Real/Virtual |
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Beyond C | inverted | reduced | real |
At C | inverted | same | real |
Between F & C | inverted | enlarged | real |
Just Beyond F | inverted | approaching infinity | real |
Just Inside F | upright | approaching infinity | virtual |
Between F & Mirror | upright | enlarged | virtual |
Location | Orientation | Size | Real/Virtual |
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Anywhere | upright | reduced | virtual |
A vertically polarized beam of light of intensity $100\frac{\text W}{\,{\text m}^2}$ passes through two polarizers. The transmission axis of the first polarizer is making an angle of 20$^\circ$ to the vertical and the second one is making an angle of 110$^\circ$ to the vertical.
A third polarizer is added before the first polarizing sheet. The transmission axis of the polarizer is making and angle of 60° to the vertical.
Now the polarizer at 60$^\circ$ is moved in between the other two polarizers.
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Two rays, emitted from the same point, diverge with an angle of 15$^\circ$ between them. The rays reflect from a plane mirror. Draw a ray diagram and find the angle between the two rays after the reflection.
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Construct the images formed by a concave mirror when the object is
Discuss the nature and relative size of each image.
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An object 2 cm in height is placed at the center of curvature C in front of a concave mirror. What is the height of its image?
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An object 1.5 cm in height is placed 7 cm in front of a concave mirror with a radius of curvature of 5 cm.
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A dentist places a mirror 1.5 cm from your tooth. He sees an enlarged image 4 cm behind the mirror.
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An auditorium has organ pipes at the front and at the rear of the hall. Two identical pipes, one at the front and one at the back, have fundamental frequencies of 264 Hz at 20$\,^\circ$C. During a performance, the organ pipes at the back of the hall are at 25$\,^\circ$C, while those at the front are still at 20$\,^\circ$C. What is the beat frequency when the two pipes sound simultaneously? (use: $v_{20\,^\circ{\text C}}=343\frac{\text m}{\text s}$, $\;\;v_{25\,^\circ{\text C}}=346\frac{\text m}{\text s}$, calculated with equation from thermodynamics: $v=\sqrt{\frac{\gamma RT}{M}}$, where M is the (average) molar mass, and $\gamma=\frac{c_p}{c_v}$ is the adiabatic constant).
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A source of sound waves of frequency 1.0 kHz is stationary. An observer is traveling at 0.50 times the speed of sound.
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A source of sound waves of frequency 1.0 kHz is traveling through the air at 0.50 times the speed of sound.
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You drive in a your car at a speed of 50 km/h and ambulance approaches from behind at a speed of 80 km/h. When the ambulance is at rest its siren produces sound at a frequency of 1050 Hz.
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The source and observer of a sound wave are both at rest with respect to the ground. The wind blows in the direction of source to observer. Is the observed frequency Doppler-shifted? Explain.
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A galaxy emits light at a wavelength of 656 nm. On earth the wavelength is measured to be 659.1 nm.
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When light having vibrations with angular frequency ranging from $2.7\times 10^{15}\frac{\text{rad}}{\text s}$ to $4.7\times 10^{15}\frac{\text{rad}}{\text s}$ strikes the retina of the eye, it stimulates the receptor cells there and is perceived as visible light. What are the limits of the period and frequency of this light?
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Microwave ovens, radio, radar, and x-rays utilize electromagnetic waves. Compare the energy, frequency and wavelengths of these waves to those of visible radiation.
A lightning flash is seen in the sky and 8.2 s later the boom of the thunder is heard. The temperature of the air is 12$\,^\circ$C. (use $v_{12\,^\circ{\text C}}=338\frac{\text m}{\text s}$) How far away is the lightning strike?
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The microwave background radiation leftover from the big bang has an average energy density of $4\times 10^{-14}\frac{\text J}{ {\text m}^3}$.
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The average intensity of the sunlight reaching the earth is $1390\frac{\text W}{ {\text m}^2}$.
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When sound waves strike the eardrum, the membrane vibrates with the same frequency as the sound. The highest pitch that typical humans can hear has a period of 50.0 $\mu$s. What are the frequency and angular frequency of the vibrating eardrum for this sound?
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High-frequency sound waves (ultrasound) are used to probe the interior of the body, much as x-rays do. To detect small objects, such as tumors, a frequency of around 5.0 MHz is used. What are the period and angular frequency of the molecular vibrations caused by this pulse of sound?
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A variable oscillator allows a laboratory student to adjust the frequency of a source to produce standing waves in a vibrating string. A 1.20-m length of string ($\mu$ = 0.400 g/m) is placed under a tension of 200 N. What frequency is necessary to produce three standing loops in the vibrating string? What is the fundamental frequency? What frequency will produce five loops?
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The piano strings that vibrate with the lowest frequencies consist of a steel wire around which a thick coil of copper wire is wrapped. Only the inner steel wire is under tension. What is the purpose of the copper coil?
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A piano string of length 1.50 m and mass density 25.0 mg/m vibrates at a (fundamental) frequency of 450.0 Hz.
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One of the harmonics of a column of air open at both ends has a frequency of 324 Hz and the next higher harmonic has a frequency of 378 Hz.
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A wave on a string has equation $y(x,t) = (4.0\,{\text{mm}}) \sin (\omega t – kx)$, where $\omega = 6.0 \times 10^2\,$rad/s and $k = 6.0\,$ rad/m.
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click: $0.04\,{\text m}\cdot\sin\!\big($ $–314\,{\text m}^{-1}\!\cdot x\big)$ | click: $0.04\,{\text m}\cdot\sin\!\big(\frac{378}{480}$ $–\,314\,{\text m}^{-1}\!\cdot x\big)$ | click: $0.04\,{\text m}\cdot\sin\!\big(378\,{\text s}^{-1}\!\cdot t\big)$ |
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During a concert a single singer generates an intensity level of 55 dB at a certain location in the concert hall. With the whole choir singing the intensity level is 75 dB. Assuming that each singer generates the same intensity level, how many people are in the choir?
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A mass of 1 kg is attached to a spring and undergoes simple harmonic oscillations with a period of 1 s. What is the force constant of the spring?
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What is the period of a pendulum formed by placing a horizontal axis (i.e. pivot point)
Assume g = 9.80 m/s^{2}.
Hint: $I_\text{cm}=\frac{1}{12}ml^2$ , Parallel axis theorem: $I=I_\text{cm}+md^2$
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A 1.5-kg mass oscillates at the end of a spring in SHM. The amplitude of the vibration is 0.15 m, and the spring constant is 80 N/m. If the mass is displaced 15 cm,
If the system is now operated on a frictionless horizontal surface,
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5. A mass is vibrating at the end of a spring of force constant 225 N/m. The figure shows a graph of its position x as a function of time t.
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