A TE uniform plane wave is incident from medium 1 with (uo, e1) on a plane interface at z 0 into medium 2 with (o, £2). Assuming e2 < E1, and 0 > 0c, %3D (a) obtain the phasor expressions for the transmitted field (E, H,), (b) verify that the average power transmitted into medium 2 is zero.

A sample of 1H in the equilibrium condition in a static magnetic field BO is excited by a short circularly polarized RF pulse. The RF pulse is a magnetic field in the transverse plane B₁(t) = B₁(t)e-i²πvot G₂ where vo is the Larmor frequency of the sample. The envelope of the RF pulse is a triangle function with parameter T: (1-7), 0≤t≤2T otherwise B₁ (t)= = { 0, (a) Find the tip angle of the magnetization vector as a function of t for 0 ≤ t ≤ 2T. (b) What is the value of T to make B1(t) a π/2 pulse?

A cloud of atoms is excited by a laser pulse and then emits electromagnetic radiation, which is detected by a spectrometer. At the detector, the amplitude of the field is given by: E(t) = E0e-i[omega]0t - t/2[tao], where E0 is a compex constant, while [omega]0 and [tao] are real constants. a) Determine the detected time-dependent intensity I(t) = |E(t)|2. b) Determine the frequency resolved intensity I([omega]) = |E([omega])|2, where E([omega]) = The integral from 0 to infinity of E(t)*ei[omega]t dt. c) Determine the frequency [omega]max where I([omega]) attains its maximum, as well as the full width at half maximum [delta omega], defined by I([omega]max +/_ [delta omega]/2) = (1/2)I([omega]max). d) Sketch the time-dependent and frequency-resolved intensities I(t) and I([omega]). Image attached with the original formatting

In the 25 ft Space Simulator facility at NASA’s Jet Propulsion Laboratory, a bank of overhead arc lamps can produce light of intensity 2500 W/m2 at the floor of the facility. (This simulates the intensity of sunlight near the planet Venus.) Find the average radiation pressure (in pascals and in atmospheres) on (a) a totally absorbing section of the floor and (b) a totally reflecting section of the floor. (c) Find the average momentum density (momentum per unit volume) in the light at the floor.