The conductivity of aluminum is 4.1×10^7 Ω−1 m−1 at room temperature. Calculate the following optical properties at 500 nm according to the Drude model. (v1 = 3.82 × 10^15 s-1 .)[1] ε1 (real parts of the complex dielectric constant)

[2] ε2 (imaginary parts of the complex dielectric constant)

[3] n (refractive index)

[4] k (damping constant)

[5] R (reflectivity)

A diverging lens has a focal length of magnitude 16.2 cm.

(a) Locate the images for each of the following object distances.
32.4 cm

16.2 cm

8.1 cm

(b) Is the image for the object at distance 32.4 real or virtual?

realvirtual    

Is the image for the object at distance 16.2 real or virtual?

realvirtual    

Is the image for the object at distance 8.1 real or virtual?

realvirtual    

(c) Is the image for the object at distance 32.4 upright or inverted?

uprightinverted    

Is the image for the object at distance 16.2 upright or inverted?

uprightinverted    

Is the image for the object at distance 8.1 upright or inverted?

uprightinverted    

(d) Find the magnification for the object at distance 32.4 cm.


Find the magnification for the object at distance 16.2 cm.


Find the magnification for the object at distance 8.1 cm.

1. A paramagnetic solid with three levels A paramagnetic solid is composed of N dipoles of magnetic moment μ⃗. The dipoles can be oriented at 0 (in alignment), 90 or 180 degree (opposite alignment) relative to an external magnetic field B⃗. The system is in equilibrium at a temperature of T. (a) Evaluate the single–particle partition function for a dipole. (b) Calculate the mean mignetic dipole moment μ. (c) Derive approximate expressions for μ in the weak–field and strong–field limits.

A thin rod (mass 8.28 kg, length 8.04 m) is sitting on a horizontal, frictionless table. There is a 0.626 kg frog sitting on the very end of the rod; you can treat the frog as a point particle. Suddenly the frog jumps off at speed 4.75 m/s, moving horizontally and perpendicular to the rod. Find ω, the angular speed of the rod after the frog jumps off, in rad/s.

The theory of the particle nature of light proposed by Isaac Newton and in order to support his theory, Newton had to explain the many behaviours of light using his theory. Discuss how Newton explained the following properties of light using this particle theory and its postulates: reflection, refraction, dispersion, rectilinear propagation, and diffraction, partial reflection-refraction.

Two thin converging lenses of focal lengths f1 = 11.0cm and f2 = 20.0cm are separated by 25.0cm. An object is placed 33.0cm to the left of lens 1. Find the position and magnification of the final image.

Elastic unequal mass collision: We have a similar situation as in the previous question but now truck A has mass mA and initial velocity uA. Truck B has mass mB and is initially at rest. The collision is elastic. (a) Show the subsequent velocities vA, vB in the laboratory frame are: vA = (mA − mB)uA/(mA + mB), vB = 2mAuA/(mA + mB). On the basis of these results, find the velocities in the two limiting cases: (i) mA >> mB; (ii) mA << mB. (b) Find the subsequent initial and final velocities u′ A, u′ B and v′ A, v′ B in the CM Frame

4. A mysterious document had been discovered in F¨uhrerbunker in Berlin and Robert Langdon was urgently called to investigate. As part of his top secret mission, at midnight he goes into a concealed archival chamber, which is sealed off from the rest of the facility by a hermetical door that will be reopened at exactly 6 am. The chamber has the volume of 2000 m3 and a primitive air circulation system with air pumped in and out at the rate of 1000 L/min. Prof. Langdon only needs two hours to examine the document. Unbeknownst to him, an agent of the powerful Rote Hakenkreuz secret society had infiltrated the security, and has managed to connect a source of carbon monoxide (CO) to the air intake. The poisonous gas is dispersed uniformly and the mixture is continuously removed via the air outflow. (a) Assuming that the concenration of CO in the air inflow is 0.5%, or 5000 ppm (parts per million), write down a differential equation for the amount A(t) of CO in the chamber as a function of time. (b) At midnight, the concentration of CO in the chamber is already 200 ppm. Set up and solve the initial value problem for A(t). (c) As a former diver, Langdon can tolerate up to 480 ppm of CO while maintaining his mental acuity and up to 1000 ppm before he passes out. Will the professor survive this ordeal and complete his mission?

The Simple harmonic oscillator: A particle of mass m constrained to move in the x-direction only is subject to a force F(x) = −kx, where k is a constant. Show that the equation of motion can be written in the form d^2x/dt2 + ω^2ox = 0, where ω^2o = k/m . (a) Show by direct substitution that the expression x = A cos ω0t + B sin ω0t where A and B are constants, is a solution and explain the physical significance of the quantity ω0. Show that an alternative solution may be expressed as x = xmax cos(ω0t + φ) where xmax is the amplitude and φ is the phase constant of oscillation. (b) Find in terms of m and ω0 the change in the potential energy U(x) − U(0) of the particle as it moves from the origin. Explain the physical significance of the sign in your result. (c) The potential energy is subject to an arbitrary additive constant; it is convenient to take U(0) = 0. The kinetic energy T(x) = 1/2mv^2. Show by differentiation that the particle’s total energy (E = T +V ) is constant. Express E as a function of the particle’s (a) maximum displacement xmax and (b) maximum velocity vmax.

Consider electric field of electromagnetic waves that are parallel to plane of incidence

find

a)   fractional ratio of reflected and refracted fields relative to incident field

b) critical angle at which reflected wave vanishes

At a wild-west show, a marksman fires a bullet at a 12 g coin that's thrown straight up into the air. The marksman points his rifle at a 45 ∘ angle above the ground, then fires a 15 g bullet at a speed of 510 m/s. Just as the coin reaches its highest point, the bullet hits it and glances off, giving the coin an exactly vertical upward velocity of 100 m/s.

At what angle measured with respect to the horizontal does the bullet ricochet away from this collision?

You have been hired as an expert witness in a court case involving an automobile accident. The accident involved a car of mass 1870 kg (car A) which approached a stationary car of mass 1020 kg (car B). The driver of car A applied his brakes 10 m before he crashed into car B. After the collision, car A slid 17 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Reconstruct the accident by calculating all the relevant velocities.

a.The speed of car A just before the breaks were applied.

b.The speed of car A just before the collision.

c. The speed of car A just after the collision.

d.The speed of car B just after the collision.

sphere with radius "a" which is made of paramagnetic material (with permeability μ) is placed in uniform magnetic field B.

Find:

a) magnetic scalar potential inside and outside of  sphere.

b) magnetization density

c) surface curent density on sphere