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_{PH203KUZMASPRING2014}
Please check your final grades, as well as the final exam solutions on D2L. Congratulations to everyone who put the effort into this course and did well! — Nicholas Kuzma 2014/06/13 23:04
Please follow this link to the survey. Once you complete it, your worst quiz grade will be replaced with 1 point. The deadline is June 9. https://docs.google.com/spreadsheet/embeddedform?formkey=dHBhZW1VbXN6UkVpX0tWYkJaYnRHVnc6MA
Exam 2 solutions are posted on D2L now under “Current exam solutions”. Please download! — Nicholas Kuzma 2014/05/16 19:51
Please email your professor if you are interested in becoming a Workshop leader next year. — Nicholas Kuzma 2014/05/10 14:15
From now on, office hour will be held at CH71, same location as the class. The time is still Thursdays 9-10am.
Project summaries will be due on Wednesday, May 28^{th}. Paper outlines are still due May 20^{th}.
4 credits at Portland State University
New! At the bottom of the sidebar on the left, there is a new link to the list of ”tasks to do” for our wiki editors (that means you!). Tick it off (by entering your username into the table) and do it!
Use WolframAlpha for calculations
Previous chapters have been moved to the sidebar:
$\cos\alpha+\cos\beta=$ $2\cos\left(\frac{\alpha+\beta}{2}\right)\cos\left(\frac{\alpha-\beta}{2}\right)$ | $\cos\alpha=\cos(-\alpha)$ | $\sqrt{1+\epsilon}\approx$ $1\!+\!\frac{1}{2}\!\epsilon$ $\sqrt{1-\epsilon}\approx$ $1\!-\!\frac{1}{2}\!\epsilon$ For small $|\epsilon|\ll 1$ | $\tan[\arcsin(x)] = \frac{x}{\sqrt{1-x^2}}$ |
$\sin\alpha=-\sin(-\alpha)$ | $\tan[\arccos(x)] = \frac{\sqrt{1-x^2}}{x}$ |
Destructive Interference: Waves cancel
$v = c/n$
Wavelength $\lambda$, of light in a medium of index of refraction $n$ greater than 1: $\lambda_n = \lambda$ (in vacuum)$ / n$
$\;\;m = 0,\, 1,\, 2,\, 3\,...$ | Refraction index order ($n_1$ and $n_2$ are on either side of the film $n_f$) | Dark fringes | Bright fringes |
---|---|---|---|
Dissimilar reflections (one extra $\pi$) | $n_1\!<\!n_f\!>\!n_2\;$ or $\;n_1\!>\!n_f\!<\!n_2$ | $t = \frac{\lambda}{2n_f}m$ | $t = \frac{\lambda}{2n_f}\left(m+\frac{1}{2}\right)$ |
Similar reflections (no extra $\pi$ or 2 extra $\pi$) | $n_1\!<\!n_f\!<\!n_2\;$ or $\;n_1\!>\!n_f\!>\!n_2$ | $t = \frac{\lambda}{2n_f}\left(m+\frac{1}{2}\right)$ | $t = \frac{\lambda}{2n_f}m$ |
Two sources emitting the light of equal wavelength, phase, and intensity, are located at positions $s_1$ and $s_2$ as shown, a short distance d apart from each other and a distance L away from the vertical screen. Find the locations of bright and dark spots on the screen in terms of the y coordinate along the screen.
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Two thin slits, 1 mm apart, are illuminated with $\lambda=750\,$nm light. The screen is $L=15\,$m away. Find the locations of the bright fringes on the screen.
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An air wedge is getting wider along $y$, such that $d(y)=\beta\!\cdot\!y$, with $\beta=10^{-5}\,$(rad). Find the spacing of interference produced by yellow ($\lambda=600\,$nm) light along the $y$ axis.
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A camera lens ($n_\text{lens}=1.42$) is coated with a thin film ($n_\text{film}=1.55$) to prevent reflections at $\lambda_\text{vac}=600\,$nm. Find the minimum thickness $d$ of the film to achieve this, assuming the (normal) reflections from both surfaces of the film, after emerging into the air, are of equal intensity.
Steps:
Use a caliper with $\frac{1\ }{1000\ }$ ${\text inch}$ gap, L$=$15m,
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Where is the question?
Find diffraction limit of the angular resolution (that is, the smallest angle between two stars that can be resolved) for a telescope with a 10-cm diameter objective lens. Assume $\lambda$ $= 600\,{\text{nm}}$
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This will resolve a 1.7-mile object on the Moon.
A laser of $\lambda=633\,$nm wavelength shines normally through a grating with thin slits every 2$\,\mu$m. Find the angle (from the original beam direction) of the 1^{st} and the 2^{nd} peaks.
Steps:
Rotations | Relativity |
---|---|
$\cos\left[\arctan\left(\frac{v}{c}\right)\right]$ $=\frac{1}{\sqrt{1+\left(\frac{v}{c}\right)^2}}$ | $\cosh\left[{\text{arctanh}}\left(\frac{v}{c}\right)\right]$ $=\frac{1}{\sqrt{1-\left(\frac{v}{c}\right)^2}}$ |
$\sin\left[\arctan\left(\frac{v}{c}\right)\right]$ $=\frac{v/c}{\sqrt{1+\left(\frac{v}{c}\right)^2}}$ | $\sinh\left[{\text{arctanh}}\left(\frac{v}{c}\right)\right]$ $=\frac{v/c}{\sqrt{1-\left(\frac{v}{c}\right)^2}}$ |
Please update if an equation is not included
How far does the light travel in 1 year? 1 minute? 1 s? 1 ms? 1 $\mu$s? 1 ns?
Steps:
Distance unit | SI equivalent (m) | Example |
---|---|---|
1 light-year | $9.5\times 10^{15}$ | $\sim\frac{1}{4}$ of the distance to the star nearest to the Sun |
1 light-minute | $1.8\times 10^{10}$ | $\sim\frac{1}{8}$ of the Earth–Sun distance |
1 light-second | $2.998\times 10^{8}$ | $\sim 75\%$ of the Earth–Moon distance |
1 light ms | $2.998\times 10^{5}$ | $186\,$miles: just beyond Seattle (from Portland) |
1 light $\mu$s | $2.998\times 10^{2}$ | $\sim 1000\,$ft from Cramer Hall to Phys. department and back |
1 light ns | $2.998\times 10^{-1}$ | $\sim 1\,$ft about the length of a page of paper |
At a speed $\;v=0.99\,c\;$ one of the two twins travels to Alpha Centauri, the nearest star (system) to our Sun, which is “only” 4.3 light-years away from us. How much older or younger is the space-traveling twin compared to the earth-bound one upon the return of the spaceship?
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A meter-stick is moving at $\;v=0.7\,c\;$ parallel to its own long dimension. How long does this stick appear from stationary Earth frame?
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A bus, moving at a speed v, turns on its headlights, emitting light at velocity c relative to the bus' frame. How fast does this light appear to travel relative to Earth?
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A spaceship, moving at a speed $\;v=0.5\,c\;$, launches a rocket in the forward direction, also at a speed $\;v=0.5\,c\;$ relative to the spaceship. How fast does the rocket appear to travel relative to our planet? How would this answer change if the rocket were fired in the backward direction, opposite to the spaceship's speed vector?
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A 50-kg atomic bomb “yields” $4\times 10^{15}\,$J of energy, assuming all of the uranium has fissioned (and not fizzled!). What percentage of the uranium mass is “converted” to energy?
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During the Chernobyl nuclear disaster in the spring of 1986, one of the dominant and most lethal radioactive isotopes released into environment was iodine-131, usually denoted ^{131}I. It has a half-life of 8 days, and spontaneously decays into a stable ^{131}Xe and an electron. The kinetic energy released in this decay is 0.971 MeV. Calculate the speed of the released electron (assuming it, being much much lighter than ^{131}Xe, acquires the vast majority of the kinetic energy). Also find the mass of such an electron, and the recoil velocity of the ^{131}Xe atom.
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Find the Schwarzschild radius of the Earth
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Is flying internationally on a passenger airplane going to delay or accelerate an atomic clock, compared to the identical clock left behind at home? Assume the speed of the airliner $\;v\approx 500\,$mph $\approx 800\frac{\text{km}}{\text{hr}}\;$, the cruising altitude 35,000 ft, and the radius of the Earth $6.4\times 10^6\,$m.
Steps:
the Word file version can be downloaded from here: chapter_30_equations.docx
An ideal blackbody absorbs all light that's incident on it. Distribution of energy in a blackbody is independent of the material, it depends only upon the temperature.
Find the peak emission frequencies of two black-body light sources, one at 4700 K (“cool white”), and another at 2700 K (“warm white”).
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The work function of potassium is $W_0=2.29\,$eV. What (if any) electron emission is observed when the blue ($\lambda=450\,$nm) or, alternatively, the red ($\lambda=750\,$nm) light strikes the metal surface?
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Find the maximum change in wavelength for blue light ($\lambda_b=450\,$nm) and for X-rays ($\lambda_X=0.1\,$nm) during Compton scattering off of electrons that are initially at rest. What percentage of the incident wavelength is this change in each case?
Steps:
In a classical model, an electron is orbiting a proton (the nucleus) in a hydrogen atom, with velocity $v=\sqrt{\frac{k_cq_e^2}{m_er}}$ $\approx 2.2\times 10^6\frac{\text m}{\text s}$, where $r=5.3\times 10^{-11}\,{\text m}$ is the radius of its orbit. Find the uncertainty of the electron's energy and momentum, and compare them to the electron's kinetic energy and momentum.
Steps:
An X-ray scattering from a free electron is observed to change its wavelength by 3.59 pm. Find the direction of propagation of the scattered electron, given that the incident X-ray has a wavelength of 0.530 nm and propagates in the positive x direction.