TRIGONOMETRY
How do you measure something that is too far away or too tall for you to stick a meter stick next to it? One way is to exploit trigonometry. If you know how far away something is and what angle it subtends, you can calculate its height. One important law of trigonometry says that the ratios of corresponding sides of similar triangles are equal, with these ratios going by the name of 'cosine', 'sine', and 'tangent'. Take a meter stick outside to measure the height of Bewkes Hall. Hold the meterstick at arm's length, with its bottom lined up with the bottom of the building. Mark on the stick where the top of the building comes to. This length is the opposite side of one of your triangles. Have your lab partner measure the distance between the bottom of your meter stick and your eye at least three different times. This is the adjacent side of that same triangle. Now measure the distance between you and the building. This is the adjacent side of the other triangle, whose opposite side is the height of the building. Calculate the height of the building. Repeat this for at least three different distances from the building, and for both lab partners. Calculate your average value for the height, plus quote an 'uncertainty', for example, "the buiding is 25± 6m tall", which means that 2/3 of your readings fall between 19m and 31m. When you are done, come inside. We will compare readings. When we are done, you should write up your results. Be sure to include (a) a sketch of your experiment, making sure to indicate your two similar triangles on the sketch, (b) whatever equations you used to calculate your height, (c) A three- to six-sentence abstract which describes what you did, what results you got, and what you think it means.

GEOMETRY: INTERIOR VOLUME OF A STYROFOAM CUP.
The formula for the volume of a cylinder is V=p r²h. Is a styrofoam cup a cylinder? If yes, measure the dimensions and calculate the volume. Otherwise, make whatever approximations make sense to estimate the volume. Measure the mass of the empty cup, and of the same cup filled with water (or use a graduated cylinder to measure the volume of the water directly). Calculate from the mass of the water what the interior volume of the cup was, and compare to what you get from measuring the linear dimesions of the cup. (1 cubic centimeter has a mass of one gram; 1 cubic meter has a mass of 1000kg.) Compare the volume in cubic centimeters to the volume in cubic meters.
 
 

 CREATIVE LITTERING
Drop a variety of different masses -- 2kg, 1kg, 100g, 10g -- from the roof of Bewkes onto the ground. Plot fall time vs mass. Make several measurements for each in order to reject any spurious data. Please drop the items onto the grass, try to avoid them hitting each other, and make sure that all items are picked up when you are done. Graph the fall time vs mass, and comment on any trends. One person in the lab can use a tape measure to measure the height from which objects were dropped. Compare the times recorded to the expected fall time assuming an acceleration of about 9.8m/s². Was Gallileo right? Was Aristotle? Explain.

 HOW FAST CAN YOU ACCELERATE?
Assuming a constant acceleration, you can measure your acceleration by measuring how far you can go in a given time interval, but it is easier to measure how long it takes to travel a given distance. Mark off distances of 2m, 4m, and 6m down the hallway and measure, with a stopwatch, how long it takes to race each distance. (Make sure to try to accelerate uniformly the entire length of your run.) Repeat each measurement a few times to verify their consistency and to be aware of the uncertainty. If you accelerate from rest, the distance you cover, assuming constant acceleration, is x=½ at². From this relation, calculate your average acceleration over 2m, 4m, 6m. Carl Lewis, the Olympic sprinter, could cover 10m in 1.88s, starting from rest. Compare Mr. Lewis' average acceleration over 10m to yours over 6m. If your calculated acceleration dropped off markedly from 2m to 6m, what conclusions would you draw?

FALLING TIMES
(1) Drop a ruler between your partner's thumb and fingers to measure how far it falls before being caught. (To make things interesting, you may try to see whether you can catch a dollar bill this way.) From this, calculate your partner's reaction time. Measure your own as well. Mark the edge of a piece of notebook paper with 1cm markings to make some measurements later in the day. See whether caffeine, or exhaustion, a full stomach, or time of day affects your reaction time. (Check at least two of these factors.) (2) If you drop two objects a fraction of a second apart, does the distance between them increase, decrease, or stay the same? Draw two parabolas, slightly displaced in the time axis, to settle this question.

GRAPHS
How many different types of graphs can one have for postion vs time for uniformly accelerated motion? Plot x vs t for cases in which the three initial parameters -- x0, v0, and a -- are each either positive, negative, or zero. Sketch the corresponding v vs t graphs. Describe in your lab notes what physical situation each example represents. Describe in words a situation in which it would be possible to have negative acceleration and positive velocity.

 VELOCITY AND ACCELERATION
Take your 'road data' -- the displacement vs time data from your recent car lab -- and create a spreadsheet in which one column consists of time in one-minute intervals. In the next column enter your displacement. Conmvert your data to MKS units. In the next column, have the spreadsheet calculate the average velocity for each minute interval. If your displacement at t=0 and t=60s are 0m and 800m, then your average velocity between 0 and 60s is 13m/s. In the next column, calculate the average accelerations. Print a graph of displacement, velocity, and acceleration vs time and record your minimum and maximum values for velocity and acceleration (indicating the units).
 
 

VECTOR EXERCISE
Consider the vectors given by A_x=10m, A_y=0m. B_x=0m, B_y=-6m. C_x=-3m, C_y=-5m.
A. Find the magnitude and direction of A, B, and C.
B. Use the magnitude and direction to graph these three vectors. Find the components of graphically and compare to the exact value.

VECTOR EXERCISE II
Draw three vectors of length 10cm on a piece of graph paper, at angles of 0, 120, and 240 degrees. Show graphically (not by solving for their components) that they add to zero.

INVERSE TUG-OF-WAR
Three volunteers from class will support a bicycle tire by pushing on it from three non-symmetrical directions. Three bathroom scales will measure the magnitudes of the forces they exert, and the instructor will mark the tire with chalk to allow the angles of the three vectors to be determined. Transfer this problem to graph paper. Calculate the magnitude of the net force, D=A+B+C, and compare the magnitude D to zero, which theory says it should equal.

SHAPE OF TWO-DIMENSIONAL TRAJECTORY
Project an image of a water fountain onto a piece of graphpaper on the wall and measure its coordinates. Put the x- and y-coordinates on a spreadsheet and see whether it can be well fit to a linear or quadratic formula. Without looking at the text or your notes, show mathematically how x and y are related. One or two groups may be given a picture of a suspension bridge to analyze. Does a parabola describe its shape?

KICKOFF TIME
We shall travel to the practise football field, because it has convenient 10yd=9.1m markings. Have one group member kick a football in the air while one member measures the time it takes to reach its maximum height, and another measures the total time it is in the air. Also measure the distance it travels down the field. Compare the two times: are they related in the way you would expect? From the total hang time and the length of the kick, calculate the initial velocity (magnitude and direction) of the kicked ball. Assume that the ball is kicked from an initial height of zero. (You can throw or kick other types of balls instead, if handy.)

CREATIVE HURLING
Each group should have one member stand on the top of Bewkes and toss some kind of ball -- a baseball, softball, or football (but no wiffleballs!) -- horizontally off the roof. Repeat several times (always with the same thrower) and get an average value for the horizontal range of the ball. Given the height of Bewkes (add about a meter to account for the ball's actual starting height), the gravitational constant, g, and the range, calculate the ball's initial speed. If the ball were thrown with the same initial speed at 45^o above the horizontal, how long would it remain in the air and how far would it travel? Test it.

PARKING-LOT PHYSICS
Measure the force needed to push a motionless car as a function of the ground (gravel, pavement, dirt/mud, etc.) and the mass (with students piled on top). If you apply an extra 5lb of force, does the car accelerate? Push the car with an extra 5lb above the frictional force, and see how far it goes in 5 seconds. Try to keep the force constant. Compare to the theoretical acceleration. (The car owner's registration should give you a clue about the car's weight.)

BATHROOM-SCALE ACCELEROMETER
Put a lab partner in a wheeled chair and use a bathroom scale to measure the force you need to exert to get this person to travel with a uniform [slow] velocity. Now push this person down the hallway with a steady force of a few pounds above what you measured before. Measure how long it takes to push the person 2m, 4m, and 6m. Plot x vs t² . You should get a straight line if it is uniformly accelerated motion. (Your instructor might want to calculate the theoretical curve, so make sure to include all the pertinent data on your lab report.)

APPARENT WEIGHT
(1) Measure the normal force supporting you as you stand on a bathroom scale on a wooden beam lying at some angle above the horizontal. Compare to what your free-body diagram predicts for this problem. (You'll need to measure the angle, q.) (2) Take a bathroom scale onto an elevator. Taking trips both up and down, record under what conditions the normal force is larger or smaller than normal. (e.g. Is the normal force larger or smaller than normal when you are travelling up but slowing down?) What force are you measuring in these two examples? Summarize your elevator results in terms of the direction of the acceleration.

COEFFICIENT OF FRICTION
Put a penny on a textbook and tilt the textbook until the penny starts to slip. Calculate from this the coefficient of static friction by measuring the angle the book makes with the horizon. Now find the angle at which the penny, if pushed, continues to slide down the textbook. From this determine the kinetic coefficient of friction. Is there a measurable difference in the two coefficients? On what do you base your answer? If there is a measurable difference, which coefficient is bigger?

CONSERVATION OF ENERGY
Suspend a spring vertically. Measure its length, L. Attach a mass to it sufficient to extend it 5cm or more. Measure the new length. Set the mass/spring system oscillating, and measure the minimum and maximum lengths of the spring. Calculate the total potential energy -- gravitational plus spring -- at the top and bottom. Is energy conserved in this experiment? (Hint: if the high point and the low point of the mass' travels are not equidistant from the stretched equilibrium point, you measured poorly. Measure it again.)

COLLISIONS: I
The enlosed picture, Fig. 16.15 from PSSC College Physics, shows a strobe photograph of two balls colliding. The center-of-mass of this two-particle system is represented by a small × for each time the strobe light was on. (a) Calculate the relative masses of the two balls. (b) Using an overhead transparency with graphpaper markings on it, calculate the x- and y-coordinates of the momentum of each ball. Take the smaller ball to have mass of "1 mu" (mu=mass unit), take the distance represented by each small block on the graph paper to be "1 block", and take the time between strobe flashes to be "1 tick". (c) Is the vector momentum conserved in this collision?

 COLLISIONS: II
Using the strobe photograph from the last lab, calculate the kinetic energies of the two balls before and after the collisions. Was this a totally elastic collision? If not, in which direction are the balls travelling?

ROCKET SCIENCE (A two-day lab)
We shall use an 'A' type Estes model rocket engine (2.5N· s impulse) a type 'B' engine (5N· s impulse), and possibly a type 'C' engine (10N· s) to launch a model rocket. Calculate the velocity of the rocket after the impulse is delivered, and use Conservation of Energy to calculate its final altitude. (We will assume that the entire impulse is delivered at t=0, with the rocket still on the ground.) We will use several independent tests to estimate its actual maximum height. Four groups of two students will stand about 100m each, in the directions of the compass, from the launch site. They will use the triangulation procedure we used earlier in the course to measure the height. Several students will measure the time it takes for the rocket to climb to its maximum height and some others will measure the total flight time -- ground to ground. Compare the various measures of maximum altitude (triangulation, rise time, theory). Are the triangulation measurements internally consistent? Do the two measurement techniques agree well with theory? Do the Estes rocket engines live up to their specs? What other conclusions can you draw?

OBSERVATIONS
1) Place one finger from each hand under a meter stick. Bringing your fingers together, find the center of mass. Try it again with one finger near the center and the other near an end. This is an amazingly easy way to find the center of mass. Why does it work? Think about the relation between normal and frictional forces, and about the relative sizes of the two normal forces when one finger is near the center of mass and the other isn't.
2) Take a spool of thread and place it on its side so that the free end of the thread passes under the spool and toward you. Pull on the thread slowly enough that the spool doesn't slip. Which way does the spool roll? Draw a free-body diagram with all the forces drawn roughly to scale -- bigger vectors drawn bigger and smaller ones smaller -- to help explain why.

CIRCULAR MOTION
Suspend a 50g mass from a long string so that the mass nearly touches the ground. Get it to travel in a horizontal circle. Measure the time it takes to travel ten times around, and the radius of its circle, and calculate its average speed. From this measure the mass' centripetal acceleration and centripetal force. Now draw a free-body-diagram and calculate the component of force pointing toward the center of the circle. Compare to the measured centripetal force. (Hint: you need to know q.)

CONSERVATION OF ENERGY -- PENDULUM
Use a rubber band and a spool of 'suture thread' to make a pendulum of at least 1m length. Measure the length from the top of the string to the center of the spool. Mount it from a rod, pull the spool away from its equilibrium, and let it swing 10 times. Have a lab partner measure the total distance of the path that it follows when it swings, and calculate the spool's average speed. For this motion (in which the acceleration is nonuniform) the maximum speed should equal 1.57 times the average speed. Calculate the maximum speed. Now, from conservation of energy, calculate what this speed ought to be. The height of the spool when it is at its maximum displacement is L(1-cosq), where L is the length of the string and q is the maximum angle the string makes with the vertical.

ROLL YOUR OWN
Given objects having the following shapes -- a hoop, a solid disc, and a sphere -- determine (a) whether the speed of an object rolling down an inclined plane depends on shape but not on size or mass, (b) the order of finish in a race between a hoop, disc, and sphere of similar size and/or mass, and (c) whether your observed answers to (a) and (b) agree with theory.
You may want to use Conservation of Energy to calculate the final speed of the object at the bottom of the incline, and then calculate the time by taking v_avg=½ v.

ANGULAR MOMENTUM
Measure your angular velocity while spinning on a rotational platform, both before and after drawing your arms in. For the case where your arms are out, assume that 13% of your mass is in your arms, which resemble a rod spinning about its center, and 87% is in a cylinder (your trunk) of unknown radius. For the other case, assume that you are a cylinder of 100% of your mass, with the same unknown radius. Now, assuming that angular momentum is conserved, calculate that radius -- the effective radius of yourself as a cylinder. Compare this to whatever direct measurement of your body you would want to compare it to. Were the assumptions made in calculating this radius reasonable? If not, which was/were suspect?

ALL MODELS HAVE THEIR LIMITATIONS
As the amplitude of a pendulum increases, the period changes slightly. Fortunately, in a pendulum-regulated clock, the amplitude is kept constant. Measure the variation of period as a function of amplitude for 0^o, 5^o, 10^o, and 20^o amplitudes. Is the effect linear, quadratic, or other? How steady must the amplitude of a small-angle pendulum be to err by no more than 1 minute per day -- 0.07%, an unacceptable amount for most people?

DON'T LEAVE YOUR SEAT
I. If you are sitting in a 'springy' chair, calculate its spring constant. Begin by oscillating up and down in your chair. Don't use your legs to push off on the chair: flap your arms like a chicken instead. Measure the time it takes to bounce ten times, calculate the period, then, using your own mass, calculate the spring constant. Repeat for your lab partner. Now calculate how far your chair should compress when you sit on it. Measure and compare. Does Hooke's model adequately describe your chair?
II. Take a 12 oz. soda can, filled with water. Hang it from a rubber band. Measure its displacement and calculate the spring constant of the rubber band (What is the mass of a 12oz. soda can?). Estimate from this the period of oscillation of the can at the end of the rubber band. Measure that period directly by forcing it to oscillate. (The internal damping of the rubber band may alter this period slightly.)

FREQUENCY and PITCH II
The choice of frequencies in the chromatic scale (twelve half-steps per octave) is not as arbitrary as it may seem. Write down all the frequencies in one octave, from 440Hz to 880Hz. If your text has a table with these numbers, use it. Now calculate the first nine overtones of middle A (f₁=440Hz), going up to 10f₁. The first overtone is 880Hz. This is just one octave above 440Hz. Boring. The second overtone is 1320Hz, which is one octave above 660Hz, which should be very close to one of the numbers in the text's table. Which note is it? Repeat for the rest of your overtones. Do any of the overtones not match your chromatic scale? If so, use the program WHINER to determine whether it is close enough to either note to be acceptable to your ear.

"MY INSTRUCTOR SUCKS/BLOWS."
Your instructor has an Erlenmeyer flask and a long length of clear tubing. S/he can use the tubing to (a) suck colored water up out of the flask, or (b) blow the water up out of the flask by increasing the pressure inside the flask. Measure the height of water that your instructor can suck or blow out of the flask. Convert these into gauge pressures -- positive for overpressures, negative for vacuums. Convert these gauge pressures into units of atmospheres. What do you conclude? Can you think of any reasons that humans might be better adapted to do one action (suck or blow) better than the other?

ARCHIMEDES
How high in the water will a vertical wooden ruler float? Measure its density by measuring its dimensions and its mass. Compare how high it floats to how high you would expect it to.

SPEED OF WATER FLOWING OUT OF A STYROFOAM CUP
Make two holes in the side of a styrofoam cup. Estimate the range of speeds of the water as it exits the cup through the lower hole, given that the height of the waater goes from the top hole to the bottom. Calculate from this where to place a bucket to catch the water as it comes out, if the cup is placed on a lab table well above the floor. Test it.

BERNOULLI DEMOS
1) Fold an index card in half, stand it like an 'A' on a table and blow underneath it. Describe what happens. Why doesn't it blow away? 2) Put a thumbtack into an index card and place it against the hole in a spool of thread. Blow through the hole. Why does the card do what it does? 3) Place a clear plastic straw in a cup full of water. By blowing across the top of the straw, raise the water level in the straw -- Sucking on the straw doesn't count. Measure the height the water rises, and calculate the speed of your breath.

SPECIFIC HEAT
Put 150mL of water in a styrofoam cup. Measure the water temperature, then put the cup in a microwave oven for a minute. Measure the water temperature immediately, making sure to stir the water with the thermometer as you do so. If a calorie (1cal=4.186J) is defined as the amount of heat it takes to raise 1mL of water by 1 Celsius degree, calculate the rate at which the oven heats, both in calories per second and in J/s or Watts. Repeat this experiment with four cups each holding 150mL of fresh tap water. Is the oven's output the same?
Is the specific heat of water really a constant with respect to temperature, that is, does it take 1 cal to raise 1mL of water 1C, regardless of temperature? To answer this question, put the cup of water back into the oven and measure its temperature before and after successive one-minute blasts in the microwave.
WARNING: The thermometer contains mercury, a metal. Never put any metals inside a microwave oven!!

LATENT HEAT
Measure the mass of a styrofoam cup with 150mL of water and its temperature. Calculate the rate at which the temperature rises in a microwave oven, as you did in the last lab. Calculate the time it would take for it to rise 100C, if it could do so without boiling. Now, heat the water to boiling, quickly measure the mass, and reheat the water for the length of time you just calculated. Measure the mass of the water after that length of time. Calculate the ratio of latent heat to specific heat, using the original mass, m, the mass lost to boiling, Dm, and the equivalent temperature rise, DT=100C.

MASS OF A BALLOON
Assuming air to be an ideal gas, calculate the pressure of the air inside a balloon by measuring its mass. Be sure to subtract off the mass of the part of the balloon which is not air. If you get a pressure less than 1atm, what physical law did you forget to apply? Recalculate the pressure. How close is the pressure to 1atm?

LAUNCHING A HOT-AIR BALLOON
Today we will inflate a 0.95 cubic meter tissue-paper hot air balloon, the shell of which has a mass of 138g. In order for the thing to float, we need to heat the air inside by about 40C above the surrounding air. (You should be able to calculate that value, but I won't ask you to.) Calculate the amount of heat needed to get the balloon to float. You will need, of course, to use the First Law of Thermodynamics, and you will be solving for Q. Measure the amount of time it takes for a blowtorch to get the balloon to lift. From this, calculate the power output of the torch in Watts. Does the answer make sense? How does it compare, for example, to the power output of a lightbulb?
CAUTION: Use a stovepipe assembly with the blowtorch to avoid a fire hazard, and remove the stovepipe from the balloo before turning off the torch. The stovepipe gets very hot once there is no air rushing through it, tissue paper burns very rapidly, and this balloon took hours to piece together.

ENTROPY
Calculate the probability of seeing 1, 2, 3, 4, or 5 'heads' after 5 throws of a coin, assuming that an individual coin toss is exactly 50% likely to yield 'heads'. How many coins would you have to toss to be able to prove whether the probability is exactly 50%?
Throw a fistfull of five coins 40 times (for a total of 200 individual coin tosses), counting the number of heads in each batch. Calculate the experimental probability of throwing 1, 2, 3, 4, or 5 'heads' out of five. Also calculate the experimental probability of throwing 5 'heads' out of ten (by grouping together adjacent data). Compare this probability to theory (63/256). Finally, calculate the total probability of tossing a head, using all 200 events in your experiment. Does this tell you anything about how averages depend on the sample size? What does all this have to do with ideal gases and physical materials? (Hint: how many "coin tosses" are there for all the molecules inside a balloon?)

LIGHT TRAVELS IN A STRAIGHT LINE?
Turn a hotplate on to about half of its maximum power. Place your head level to the hotplate, and look across the hotplate at other objects. Set up a laser at least 2m from the hotplate, no more than 1cm higher than the hotplate, and aim it to partly reflect off the far end of the hotplate. Measure the height of the laser, the hotplate, and the spot on the wall (relative to the floor). Move the hotplate out of the way and measure how far the hotplate had deflected the laser beam.
RESULTS: Describe the appearance of objects as viewed by looking over the hotplate: which way is the light bent? Sketch it. Describe the appearance of the laser beam on the wall when it passes over the plate. Measure the distance, and angle, by which the beam is deflected by the hotplate. If this were a case of total internal reflection at a single interface, use the deflection to calculate the ratio of the indices of refraction at room temperature and close to the plate. (The index of refraction in air is 1.00027 at 20^oC and 1.00023 at 60^oC.)

FIBER OPTICS
Your instructor will show you how to couple light into an optical fiber. Be sure to move the position of the end of the fiber (in all three directions!) in order to maximize the signal coming out the other end. When you are happy with your results, see whether you can shine the output of the fiber onto an index card. You should see a bright circle which corresponds to a cone of light exiting the fiber. The cone's angle is the critical angle for total internal reflection in the fiber. Measure this angle (at least four times between you). Assuming the core of the fiber to be around 1.5 in refractive index, calculate the percentage difference in the refractive indices of core and cladding.

RAINBOW OPTICS
Take a small beaker of water and add a dash of powdered milk to make the water cloudy. Shine a laser horizontally through the beaker. If the beam does not hit the beaker square-on, it will bounce around inside the beaker a few times. Locate the second place where the beam leaves the beaker. As you increase or decrease the distance between where the laser beam enters the beaker and the center of the beaker, this outgoing beam will first move one way, then the other. Verify this! Locate this turn-around point. Put a large piece of paper underneath the beaker and mark it so that you can draw the beam's path. Measure the angle between the original and outgoing beams. Is it close to the reported 42^o angle between the center of a rainbow and the rainbow itself? Find the second rainbow, which is the beam which bounces around one more time inside the beaker. By what angle is it deflected? Protecting your eyes from other group's laser beams, shine a flashlight into your beaker and look for an actual rainbow at the same angle you found the primary rainbow.

RAY TRACING PRACTICE
You will be asked to draw ray tracing dragrams for a few problems involving lenses. In each case, draw the problem on a piece of graph paper, locating the image. Describe the image as real or virtual, upright or inverted, enlarged or reduced.
a) An object is located 3m away from a converging lens of focal length 1m.
b) An object is loated 3m away from a diverging lens of focal length -1m.
c) An object is located 1m away from a converging lens of focal length 3m.

LENSES
Draw a ray diagram for the following problem: A converging lens has a focal length of 20.0cm. Locate the image for an object distance of 30.0cm. State whether the image is real or virtual, upright or inverted, and find the magnification.
Each lab table has on it an optical bench with a lens holder and a screen. The separation of the lens and screen can be read off the scale on the side of the bench. Use light rays coming from infinity (objects outside the window -- other buildings or clouds -- are at about infinity for our purposes, that is, the light rays from them are just about parallel when they encounter the lens) to find the focal length. Based on a ray tracing diagram and the thin-lens equation, predict the locations and magnification of the image for object distances of 1.5f. Then set your "object" at the distance and measure the location of the image.

WAVE DOUBLE-SLIT INTERFERENCE VIA MOIRE INTERFERENCE
Take two transparencies with identical ripple patterns to determine the location of the interference maxima and minima relative to the two slits from which the different patterns emerge. Is the pattern at q=90^o constructive or destructive when the slits are an integer number of wavelengths away (i.e. d=kl, where k is some integer)? What is the maximum "order", m, of the bright interference fringes? Does this agree qualitatively with the equation for bright interference fringes? Measure the angles for d=4.5l. Compare with theory.

DOUBLE-SLIT AND SINGLE-SLIT INTERFERENCE
There will be a couple of lab setups in which a two-slit pattern or a single slit is set up in front of a 633nm HeNe laser. Measure the angle between successive dark spots for either case, and calculate (a) the distance between the two slits, or (b) the width of the single slit. Check whether the dark bands are equidistant for the two-slit effect, and whether the center bright band is twice as wide as the others for the single-slit effect.