1. In your own words, explain why a single interaction between two particles may be represented with more than one possible Feynman diagram

I need 3 & 4... free free to answer 1 & 2 if you want!

Lenses may be simple ones with two spherical curved surfaces on a piece of transparent material like glass or plastic, or much more complex and compounded of different elements each with sometimes a different material. The surfaces do not have to be spherical, and manufacturing techniques today allow combining these "aspheric" lenses in designs that produce exquisite detail in an image. Your cell phone camera lens is an example, as are the lenses of a larger digital or photographic camera. This week's problem is chosen to get to the basics of lenses and how they work because they are the most common essential component of optical instruments. Starting with Snell's law, you can show that a lens has a property called a "focal length" such that 1/f = 1/p + 1/q where p is the distance to the object in front of the lens, and \(q\) is the distance from the lens to the image it forms. This applies to a lens so thin that the thickness of the glass is small compared to these distances. Light from infinity must form an image at q = f Written this way, there is a convention to measure the distance to the object as positive to the left of the lens, and the distance to the image as positive to the right of the lens.

1. Where does light coming from a distance f in front of the lens form an image? Explain.

2. If I want a lens to be halfway between an object and a screen where the image forms, what is the focal length of the lens? You may answer generally, or if you prefer a specific case let the object and the screen be 10 cm apart.

3. The focal length of a thin lens is given by the "lens maker's equation" 1 divided by f space equals space left parenthesis n minus 1 right parenthesis space left parenthesis 1 divided by R subscript 1 space minus space 1 divided by R subscript 2 right parenthesis This works when you can neglect the spacing between the surfaces, that is, when the radii are much bigger than the thickness of the lens. It is simple enough, but perilous for problems because of how the signs have to be interpreted. A lens surface that curves outward so that it is thicker at the center on that surface is "convex". One that curves inward, making it thinner at the center on that side, is concave. By convention, the sign of \(R\) is positive if the lens is convex to the incoming light, and negative if it is concave. Here n is the index of refraction of the glass relative to the medium it is in (say air), and the \(R\)'s are the radii of the surfaces of the lens. Thinking of light as coming from the left, the radius is positive if it is convex to the left, concave to the right. For example, a lens that has convex surfaces on both sides with radii 10 cm, an index of 1.5, would have a focal length of 1/f = (1.5 - 1) (1/10 - (-1/10)) = 0.1 f = 10 cm The second radius is negative because it is concave to the left and convex to the right. The shape of the surface and the index on both sides determine whether the lens converges the light, or diverges it.

--> 3. What would be the radius of curvature of the surfaces of a double convex lens with the same shape on both sides and a focal length of 1 meter? Assume an index of 1.5.

--> 4. Suppose you made a lens in which the first surface was convex to the left with a radius of 50 cm. Immediately after it the back surface is exactly the same, also convex to the left, with the same radius of curvature. Now take this lens outside and let sunlight fall on it. What happens to the light that goes through the lens? Explain it with these equations for a thin lens, and also with the wave theory of light.

You are asked to define 10 different " The right hand rule". Here you first define the application and explain how the right hand rule is applied to find the direction of physical concept.

For good battery performance and economics, each component in battery has several requirements. Write the requirements of cathode, anode and electrolyte of Li-ion battery.

Plotting rotational variables

Continuing on with using the human body as a physics apparatus, it’s time to try an experiment with your leg!  First, find a comfortable place where you can sit and swing your legs freely.  This could be an office chair which you raise to the point where your feet do not touch the ground, a table top (which can support your weight!), picnic table, or any other location where you sit and swing your legs freely from your knees.

Your task is to create a sketch of your foot’s motion as you GENTLY swing your foot from directly under you, to a fully extended position.  Try rocking your foot back and forth a few times and imagine how the foot’s angular displacement, velocity, and acceleration are changing over time.  Imagine that the angular displacement is zero when your foot is resting directly underneath you.

8.  In the space below, make a sketch of angular displacement, , as a function of time as you slowly and steadily bring your foot from beneath you, to the extended position. Appendix A has a nice review of how to sketch a plot of “something” vs. “another thing”.  You may find the drawing functionin Google docs useful in creating the plot. Or you can sketch it out on paper and attach a photograph of the sketch, your preference.

.  In the space below, make a sketch of angular velocity vs. time of your foot as you slowly and steadily bring your foot from directly underneath to straight out from the knee.

10.   In the space below, make a sketch of angular acceleration vs. time of your foot as you slowly and steadily bring your foot from directly beneath you, to straight out.

Four displacement vectors, A, B, C, and D, are shown in the diagram below. Their magnitudes are:  A = 16.2 m, B = 11.0 m, C = 12.0 m, and D =  24.0 m

What is the magnitude, in meters, and direction, in degrees, of the resultant vector sum of A, B, C, and D?

Give the direction as an angle measured counterclockwise from the +x direction.

From Chapter 2 (Motion Along A Straight Line) select and explain in your own words two of the following 6 learning goals. Then find someone else post discussing a different learning goal than you explained, review their explanation and add anything they may have missed that you feel is important.

2.1 - How do the ideas of displacement and average velocity help us describe straight line motion?

2.2 - What is the meaning of instantaneous velocity; and what is the difference between velocity and speed?

2.3 - How does one use average acceleration and instantaneous acceleration to describe changes in velocity

2.4 - How does one use equations and graphs to solve problems that involve straight-line motion with constant Acceleration?

2.5 - How does we go about solving problems in which an object is falling freely under the influence of gravity alone?

2.6 - How does one analyze straight-line motion when the acceleration is not constant?

please type your answer you don't have to draw just type it

Why are satellites normally sent into orbit by firing them in an easterly direction? Based on this, explain why the International Space Station (ISS) orbits the Earth at about 17,500 miles per hour at an altitude above Earth’s surface of about 230 miles. Would it be more efficient to have a higher or lower orbit for the ISS? Explain in detail why or why not.

Consider an X-ray beam of wavelength 0.1 nm and a gamma ray beam of wavelength 0.00188 nm. if each is scattered by an angle of 90 degrees by a free electron, what is the compton shift in the wavelength of the rays? in each case also determine the kinetic energy transferred to the recoiling electron and how much of the incident energy in the rays is lost.

23. Consider a 2D spacetime whose metric is: ds^2 = −dt^2 + [f(q)]^2 dq^2 (3) where f(q) is any function of the spatial coordinate q. a) Show that the t component of the geodesic equation implies that dt dτ is contant for a geodesic. b) The q component of the geodesic equation is hard to integrate, but show that requiring u · u = −1 implies that f dq dτ is a constant for a geodesic. c) Argue then that the trajectory q(t) of a free particle in this spacetime is such that dq dt = constant f . d) Imagine that we transform to a new coordinate system with coordinates t and x where x = F(q) and F(q) is the antiderivative of f(q). Show that the metric in the new coordinate system is the metric for flat spacetime, so the spacetime described by equation 3 is simply flat spacetime in disguise. We know geodesics in flat spacetime obey dx dτ = (f dq) dτ = constant, so the result in part b) is not surprising.

A pendulum has a length 1 m and a mass 1 kg. Assume Earth free fall acceleration equal to 10 m/s^2. When the pendulum oscillates, the maximal deflection angle is +/-1 degree.

1.Suppose the pendulum started losing energy at the rate 1% per period. As a result, the energy of the pendulum drops according to E(t)= E(t=0)*exp(-z*t). Let’s call z damping constant, it has units 1/sec.

a) Find Z

b) Sketch E(t) for the time span of a few hundred periods.

c) How long will it take before the energy drops to half of the initial value at t=0?

d) How long will it take before the max deflection angle drops to half of the initial value at t=0?

e) If the damping was produced by a force given by F = -v*k, where v is the velocity and k is some friction coefficient, find k.

f) Suppose you are aiming to excite a resonance of this pendulum by kicking it with a periodically modulated force at a frequency f. What should be f in Hz and approximately how accurately should you be able to adjust f, i.e. f +/-how much?