20150329

Physics midterm problem: object distance with greatest magnification

Physics 205B Midterm 1, spring semester 2015
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 23.63

An object can be placed either 16 cm or 14 cm in front of a f = +15 cm converging lens. Decide which object distance will result in the largest image (regardless of being real/virtual, or inverted/upright), or if there will be a tie. Show your work and explain your reasoning using the properties of lenses, thin lens equations and/or ray tracings.

Solution and grading rubric:
  • p:
    Correct. Compares the linear magnification ratios of both object distances using one of two methods:
    1. determines the image distances produced by these objects, then sets up the ratio m = –di/do to find their respective linear magnification factors;
    2. a carefully, properly scaled ray tracing diagram.
  • r:
    Nearly correct, but includes minor math errors. May have sign errors or inverse errors.
  • t:
    Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least enough steps are shown that would theoretically result in a complete answer, multiple errors (or omission of last step of finding m = –di/do ratio) notwithstanding. May draw a ray tracing diagram that does not have its object distances properly scaled with regards to the focal points, but at least makes a consistent conclusion based on the faulty scaling of object positions.
  • v:
    Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Ray tracings have real images for both cases, etc.
  • x:
    Implementation/application of ideas, but credit given for effort rather than merit.
  • y:
    Irrelevant discussion/effectively blank.
  • z:
    Blank.
Grading distribution:
Sections 30882, 30883
Exam code: midterm01p34K
p: 21 students
r: 6 students
t: 13 students
v: 6 students
x: 1 student
y: 0 students
z: 0 student

A sample "p" response (from student 8984):

20150327

Astronomy quiz archive: solar system

Astronomy 210 Quiz 4, spring semester 2015
Cuesta College, San Luis Obispo, CA

Section 30674, version 1
Exam code: quiz04NoR3


Section 30674
0- 8.0 :  
8.5-16.0 :   ******* [low = 12.0]
16.5-24.0 :   *************** [mean = 23.5 +/- 6.6]
24.5-32.0 :   ***********
32.5-40.0 :   ***** [high = 36.5]

Section 30676, version 1
Exam code: quiz04s0U7


Section 30676
0- 8.0 :   * [low = 8.0]
8.5-16.0 :   **********
16.5-24.0 :   ************** [mean = 24.4 +/- 8.6]
24.5-32.0 :   ************
32.5-40.0 :   ********** [high = 40.0]

20150319

Presentation: star brightnesses

Look at these stars. Just look at them. And let's sort them by their brightnesses. But just their brightnesses, as we're going to ignore the colors of these stars (even though they do have different colors), and we're going to ignore the sizes of these stars as well (even though they do have different sizes). This is why the stars are represented here as squares that correspond to their relative brightnesses.

In this presentation we will discuss how star brightnesses are measured, and how we can determine whether a bright star or a dim star seen in the night sky is really bright or dim (or perhaps not really bright or dim).

Star brightnesses are measured using a magnitude scale, with +1 for bright stars, and +6 for the dim stars. If the smaller positive number for brighter stars bothers you, think of ranking schemes (as did the ancient Greeks in originally setting up this scale), where the brightest stars are "first place" or "top tier" stars, and the dimmest stars are in "sixth place" or "bottom tier" stars. And the scale did need to get revised, as there a few stars that blow the top off the original +1 to +6 scale. Brighter than the "first place" +1 stars are "zero place" stars, and brighter than those stars are "–1 place" stars. These are the very bright stars, and the scale has larger negative numbers for progressively brighter stars. There are also lots of stars dimmer than +6, and the scale has larger positive numbers for progressively dimmer stars.

The apparent magnitude m (lower case italics "m") of a star is the "as is" brightness as seen by an observer on Earth, without compensating for distance. The sun is not the brightest star ever, but being extremely close makes it seem brighter than all other stars. Deneb is one of the brightest stars ever, but being extremely far away makes it seem dimmer than many other stars. So, apparent magnitude is not really a fair way to compare the brightnesses of stars, as some stars cheat (like our sun), and some stars get dissed (like Deneb).

In order to compensate for the effect of distances on star brightnesses, we need to be able to measure their distances. This is done using parallax, which is the shift in perspective as you look at an object from two different viewpoints, such as Diane Lane's left eye and right eye in Under the Tuscan Sun (Blue Gardenia Productions/Buena Vista Pictures, 2003).

In astronomy the two different viewpoints for looking at a star is from Earth when it is at one end of its orbit, then six months later from Earth when it is at the other end of its orbit. In this case the nearby star will appear to shift back and forth, and the amount of this shift (its parallax) can be related to its distance.

Again we look at a star from Earth when it is at one end of its orbit, then six months later from Earth when it is at the other end of its orbit, but this time the star is farther away. In this case the distant star will appear to shift back and forth a smaller amount, and the smaller amount of this shift (a smaller parallax) can be related to a greater distance. In practice, this shift is an angle measured not in degrees, but in very small units of arc seconds (where 1 arc second is 1/3,600th of a degree), and a star that shifts by 1 arcsecond corresponds to being at a distance of 1 parsec away ("a parallax angle of 1 arc second"), or 3.26 light years away. Parallax shifts bigger than 1 arc second would correspond to stars closer than 1 parsec away, while parallax shifts smaller than 1 arc second would correspond to stars farther than 1 parsec away.

Now that we have one method (actually several other methods are also used) to determine how close or how far away a star is, we can then determine the actual brightness of a star by compensating for its distance. In the case of the sun, we know that it is extremely close, and if we conceptually push it back to an arbitrary "fair comparison distance" of 10 parsecs away, it will get dimmer.

Similarly for Deneb, we know that it is extremely far away, and if we conceptually bring to closer to the arbitrary "fair comparison distance" of 10 parsecs away (just like we did for the sun), it will get brighter.

And now that we have compensated for the extreme closeness of the sun and the extreme distance of Deneb by conceptually relocating them to the same "fair comparison distance" of 10 parsecs away, we can see that the sun is actually much dimmer than Deneb. The brightnesses of stars when placed 10 parsecs away is their absolute magnitude M (actually, upper-case cursive "M"), and if we conceptually relocate every other star to 10 parsecs (once we know their actual distances), absolute magnitude becomes a way to compare the "actual" brightnesses of stars with each other, something that will be important in the next presentation on star temperatures and sizes.

Let's practice applying these concepts to some stars.

Rank these stars from brightest to dimmest, as seen from Earth:
______, _____, _____, _____.

Rank these stars from brightest to dimmest, if relocated to 10 parsecs from Earth.
______, _____, _____, _____.

List the star(s) (if any) that get dimmer when relocated from their original positions to 10 parsecs from Earth (these are the stars that are located nearer than 10 parsecs from Earth).
______, _____, _____, _____.

List the star(s) (if any) that get brighter when relocated from their original positions to 10 parsecs from Earth (these are the stars that are located farther than 10 parsecs from Earth).
______, _____, _____, _____.

20150315

Astronomy midterm question: meridian zodiac sign at sunset?

Astronomy 210 Midterm 1, spring semester 2015
Cuesta College, San Luis Obispo, CA

An astronomy question on an online discussion board[*] was asked and answered:
f_14: Which constellation of the zodiac is highest in the sky at sunset tonight? Explain how you deduced the answer.
p_b: Gemini. The sun is now in Pisces today and since that constellation sets with the sun, at that point of time Gemini is at the zenith.
Discuss a plausible date and time for an observer in San Luis Obispo, CA to find these positions of Gemini and Pisces. If there is no such plausible date and time, then explain why. Defend your answer by clearly explaining how you used your starwheel to do this, along with any assumptions that you may have made.

[*] answers.yahoo.com/question/index?qid=20100916125243AABASB3.

Solution and grading rubric:
  • p:
    Correct. Discussion for plausible date/time includes the following:
    1. determines when Pisces would be the sun-sign, by setting Pisces at the meridian, and finding the date what would correspond to 12 PM (March 30);
    2. sets Pisces on the west horizon of the starwheel such that it (and the sun) is setting;
    3. verifies that Gemini is at the meridian at that time on March 30 (around 7 PM).
  • r:
    Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. Has two of the three discussion points in (p).
  • t:
    Contains right ideas, but discussion is unclear/incomplete or contains major errors. Has only one of the three discussion points in (p).
  • v:
    Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Some related discussion of using starwheel to find sun-signs, diurnal motion (rising/setting).
  • x:
    Implementation/application of ideas, but credit given for effort rather than merit.
  • y:
    Irrelevant discussion/effectively blank.
  • z:
    Blank.
Grading distribution:
Section 30676
Exam code: midterm01sh3P
p: 33 students
r: 8 students
t: 6 students
v: 5 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 7495):

Another sample "p" response (from student 7495):

Astronomy midterm question: Libra sun-sign with Gemini rising

Astronomy 210 Midterm 1, spring semester 2015
Cuesta College, San Luis Obispo, CA

An astronomy question on an online discussion board[*] was asked and answered:
??: Okay, I have a Libra sun-sign and a Gemini rising sign. Someone please explain what they mean!
fk: The sun sign is technically the sign the sun was in on the day you were born, and the rising sign was the sign rising on the horizon at the time of day you were born.
Discuss a plausible date and time for an observer in San Luis Obispo, CA to find the sun in Libra, with Gemini rising. If there is no such plausible date and time, then explain why. Defend your answer by clearly explaining how you used your starwheel to do this, along with any assumptions that you may have made.

[*] answers.yahoo.com/question/index?qid=1006041109420.

Solution and grading rubric:
  • p:
    Correct. Discussion for plausible date/time includes the following:
    1. determines when Libra would be the sun-sign, by setting Libra at the meridian, and finding the date what would correspond to 12 PM (November 10);
    2. sets Gemini on the east horizon of the starwheel such that it is rising;
    3. looks at the time (around 8 PM to 9 PM) on November 10 that corresponds to when Gemini would rise.
  • r:
    Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. Has two of the three discussion points in (p). May find when Libra is the sun-sign, but adds additional restriction that Libra (and the sun) must still be visible in the sky when Gemini is rising, which is not possible.
  • t:
    Contains right ideas, but discussion is unclear/incomplete or contains major errors. Has only one of the three discussion points in (p).
  • v:
    Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Some related discussion of using starwheel to find sun-signs, diurnal motion (rising/setting).
  • x:
    Implementation/application of ideas, but credit given for effort rather than merit.
  • y:
    Irrelevant discussion/effectively blank.
  • z:
    Blank.
Grading distribution:
Section 30674
Exam code: midterm01nR31
p: 4 students
r: 22 students
t: 11 students
v: 0 students
x: 1 student
y: 0 students
z: 0 students

A sample "p" response (from student 7495):

A sample "r" response (from student 7897) discussing Gemini setting, instead of rising:

A sample "r" response (from student 0104), with a diagram showing Gemini setting (and not rising):

Astronomy midterm question: "midnight clear" moon inscription?

Astronomy 210 Midterm 1, spring semester 2015
Cuesta College, San Luis Obispo, CA

The image at right posted by REI[*] depicts the moon at night, with the inscription "Midnight Clear." Discuss whether or not this "midnight" inscription and moon image is plausible, and how you know this. Support your answer using a diagram showing the positions of the sun, the moon, Earth, and an observer on Earth.

[*] Daniel Bear Hunley, blog.rei.com/social/hand-lettering-art-mobile-wallpaper-beauty-go/.

Solution and grading rubric:
  • p:
    Correct. The waning crescent moon (less than the left half of the moon is lit up) is highest overhead at 9:00 AM, and would have risen six hours before at 3:00 AM, such that it would be impossible to see at midnight. (May identify the moon as third quarter (highest overhead at 6:00 AM, which would rise at midnight), and may argue that the moon is either visible or not visible at midnight.) Complete diagram and reasoning.
  • r:
    Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. Diagram and/or explanation has minor errors.
  • t:
    Contains right ideas, but discussion is unclear/incomplete or contains major errors. Problems with either diagram or discussion.
  • v:
    Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Diagram and discussion problematic.
  • x:
    Implementation/application of ideas, but credit given for effort rather than merit.
  • y:
    Irrelevant discussion/effectively blank.
  • z:
    Blank.
Grading distribution:
Section 30674
Exam code: midterm01nR31
p: 23 students
r: 3 student
t: 6 students
v: 5 students
x: 1 student
y: 0 students
z: 0 students

A sample "p" response (from student 9507), arguing why this waning crescent moon picture would not be possible:

A sample "p" response (from student 7606), arguing why this third quarter moon picture could be possible:

A sample "p" response (from student 4294), discussing the impossibility of both third quarter and waning crescent moon interpretations of this photo:

Astronomy midterm question: Zion National Park moon Instagram

Astronomy 210 Midterm 1, spring semester 2015
Cuesta College, San Luis Obispo, CA

The image at right[*] posted on the Instagram account of the U.S. Department of the Interior depicts a moon low above a horizon during the day. Discuss whether or not this moon image is plausible, and how you know this. Support your answer using a diagram showing the positions of the sun, the moon, Earth, and an observer on Earth.

[*] instagram/p/mYnT4Ngu04/.

Solution and grading rubric:
  • p:
    Correct. The waning gibbous moon (more than the left half of the moon is lit up) is highest overhead at 3:00 AM, and would have risen six hours before at 9:00 PM, and set six hours later at 9:00 AM. In order for this picture to have been taken during the day, the time would need to sometime between after sunrise at 6:00 AM, and when the waning gibbous moon would set at 9:00 AM. Complete diagram and reasoning.
  • r:
    Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. Diagram and/or explanation has minor errors.
  • t:
    Contains right ideas, but discussion is unclear/incomplete or contains major errors. Problems with either diagram or discussion.
  • v:
    Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Diagram and discussion problematic.
  • x:
    Implementation/application of ideas, but credit given for effort rather than merit.
  • y:
    Irrelevant discussion/effectively blank.
  • z:
    Blank.
Grading distribution:
Section 30676
Exam code: midterm01sh3P
p: 28 students
r: 8 student
t: 9 students
v: 3 students
x: 4 students
y: 0 students
z: 0 students

A sample "p" response (from student 3562):

Astronomy midterm question: "evening stars" visible as "morning stars?"

Astronomy 210 Midterm 1, spring semester 2015
Cuesta College, San Luis Obispo, CA

A view of the San Luis Obispo, CA sky is shown below for September 9, 2015 with the planets Saturn and Mercury.


Discuss which of these planets will be visible at sunrise the next day. If neither planet will be visible, then explain why. Support your answer using a diagram showing the positions of the sun, Saturn, Mercury, Earth, and an observer on Earth.

Solution and grading rubric:
  • p:
    Correct. Complete diagram (with the sun, Saturn, Mercury, and an observer on Earth), and discusses/demonstrates:
    1. places Saturn somewhere in an outer orbit such that it is visible high overhead at sunrise, and Mercury somewhere in an inner orbit to be low over the western horizon of the observer at sunset;
    2. at sunrise 12 hours later, Saturn and Mercury will both essentially be in their same locations in their orbits;
    3. thus both Saturn and Mercury would be below the horizon for an observer on Earth at sunrise, and thus not be visible.
  • r:
    Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. Two of three points (1)-(3) correct, one is problematic/incomplete.
  • t:
    Contains right ideas, but discussion is unclear/incomplete or contains major errors. Problems with either diagram or discussion. One of three points (1)-(3) correct.
  • v:
    Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Diagram and discussion problematic.
  • x:
    Implementation/application of ideas, but credit given for effort rather than merit. Misconceptions or non-relevant concepts.
  • y:
    Irrelevant discussion/effectively blank.
  • z:
    Blank.
Grading distribution:
Section 30674
Exam code: midterm01nR31
p: 8 students
r: 10 students
t: 12 students
v: 8 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 0622):

Astronomy midterm question: "evening stars" visible as "morning stars?"

Astronomy 210 Midterm 1, spring semester 2015
Cuesta College, San Luis Obispo, CA

A view of the San Luis Obispo, CA sky is shown below for June 10, 2017 with the planets Jupiter and Mars.


Discuss which of these planets will be visible at sunrise the next day. If neither planet will be visible, then explain why. Support your answer using a diagram showing the positions of the sun, Jupiter, Mars, Earth, and an observer on Earth.

Solution and grading rubric:
  • p:
    Correct. Complete diagram (with the sun, Jupiter, Mars, and an observer on Earth), and discusses/demonstrates:
    1. places Jupiter somewhere in an outer orbit such that it is visible high overhead at sunrise, and Mars somewhere in an outer orbit to be low over the western horizon of the observer at sunset;
    2. at sunrise 12 hours later, Jupiter and Mars will both essentially be in their same locations in their orbits;
    3. thus both Jupiter and Mars would be below the horizon for an observer on Earth at sunrise, and thus not be visible.
  • r:
    Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. Two of three points (1)-(3) correct, one is problematic/incomplete.
  • t:
    Contains right ideas, but discussion is unclear/incomplete or contains major errors. Problems with either diagram or discussion. One of three points (1)-(3) correct.
  • v:
    Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Diagram and discussion problematic.
  • x:
    Implementation/application of ideas, but credit given for effort rather than merit. Misconceptions or non-relevant concepts.
  • y:
    Irrelevant discussion/effectively blank.
  • z:
    Blank.
Grading distribution:
Section 30676
Exam code: midterm01sh3P
p: 13 students
r: 11 students
t: 14 students
v: 9 students
x: 5 students
y: 0 students
z: 0 students

A sample "p" response (from student 1212), with an observer lying prone on the ground:

20150314

Physics quiz archive: interference, electrostatics

Physics 205B Quiz 3, spring semester 2015
Cuesta College, San Luis Obispo, CA
Sections 30882, 30883, version 1
Exam code: quiz03wJnb



Sections 30882, 30883 results
0- 6 :   ****** [low = 0]
7-12 :   *****
13-18 :   ****************** [mean = 16.7 +/- 7.2]
19-24 :   ***********
25-30 :   **** [high = 30]

20150311

Presentation: circuit basics

Wet plywood. Wires clipped to nails. Wires connected to a source of 15,000 volts. What could be more beautiful than this basic circuit? Or dangerous? (Video link: 15,000 volts.")

In this presentation we will take a first look at the basics of basic circuits. As with the set-up above, some of these very basic circuits are also very dangerous, so unless you absolutely know what you're doing (that is to say, you know enough physics to understand the perils involved), do not try these at home!

The most basic circuit we can build will have an ideal "electromotive" (emf) source of voltage connected to a resistor, such that charges can flow continuously around and around. Peculiarly the definition of current is the amount of positive charge (in coulombs (C)) that circulates per time (in seconds (s)), and these units of C/s are defined as amps (A). But as discussed in a previous presentation, in a conductor it is actually the negatively charged electrons that are free to move. So by convention we refer to "current" flowing clockwise through this circuit, while the electrons actually circulate in the opposite counterclockwise direction through this circuit. Just keep watching this GIF animation for a while until you get used to those current direction concepts. More on emf sources and resistors below, when you're ready.

An ideal battery uses chemical reactions that exchange charges in order to release electric potential energy, giving potential (that is, electric potential energy per charge, or voltage, measured in volts (V)) to the charges that circulate in a circuit.

Different chemical reactions will release different amounts of electric potential energy per charge, and thus different amounts of voltage. Note that these different batteries all have the same "AA" size, but the different chemical reactants inside (nickel metal hydride (NiMh), alkaline, or lithium) release different amounts of voltage (∆V = 1.2 V, 1.5 V, or 3.6 V, respectively). (Ideally the amount of voltage provided will be constant; but later we'll consider the effects of depleting the reactants inside "real" batteries, and the effect this has on their actual voltage output over time.)

Some larger voltage batteries are made up of a combination of individual batteries, in order to "stack" the voltage output ∆V, which is cumulative provided that their terminals are connected (+) to (-), etc. The result of stacking six individual 1.5 V alkaline batteries results in a single 9.0 V battery, as seen in several different stacking configurations.

The other part of a basic circuit is a resistor, which uses up voltage (electric potential energy per charge) as current flows through it. Different types of materials and shapes and sizes will result in different resistance values, measured in ohms (Greek letter Ω). (This is the inverse of conductance, so a good conductor (such as a metal wire) will have a low resistance value, while a poor conductor (such as an insulator) will have a high resistance value.)

If several resistors (here, Christmas light bulbs) are strung together in a line, forcing current to flow through each one in turn, then the equivalent resistance is their individual resistances added together. (This is not the only possible way to wire together resistors, but we'll stick to this basic configuration for now.)

Ohm's law can be applied to a basic circuit to determine how much current will flow in it, given the total amount of voltage from ideal batteries, and the equivalent resistance of all the resistors. Note how the different units are related in Ohm's law: a volt over an ohm is equivalent to an ampere, etc. (After a certain point you will just have to trust that all these units will work out in the end.)

So let's look at some very basic, very dangerous circuits.

We can use a wire (which has a very low resistance) to complete a basic circuit, connecting it to the (+) and (-) terminals of a 9.0 V (ideal) battery. Note the very small spark of current that leaps across the gap just as the wire completes the circuit. Now an absurd configuration of 244 9.0 V batteries are stacked with (+) terminals to (-) terminals. (How much emf voltage is that?) When a wire is connected to complete this stacked battery circuit, how does the amount of emf voltage compare to the single 9.0 V battery circuit? How does the amount of current compare to the single 9.0 V battery circuit? (Video source: "Fun with a few 9V batteries. (244 of them).")

Our next very dangerous basic circuit involves deionized water, itself a relatively poor conductor, as there are no free charges in it to transport current, so connecting a basic circuit of water with a household 120 V outlet as an emf source (where the light bulb is used to indicate the amount of current that is flowing) doesn't yield much current. When salt is poured into the water, introducing charged sodium (Na+) and chloride (Cl-) ions, how did the amount of resistance of this circuit change? How did the amount of current through this circuit change? (Video source: "Experiment electricity with saltwater.")

Our last very dangerous basic circuit is a power transformer used as an emf source, with a metal screw used to complete the circuit. This will result in a "short circuit," which is due to a very large or very small resistance? Does a very large or very small current result? (Video source: "The Metal Melter.")

In subsequent presentations we will go over more specific rules of circuit analysis for more complex configurations of emf sources and resistors, and power dissipation.