using the complex form of a electromagentic wave, derive the jones vector ans show the normalisation of the general vector.
using the complex form of a electromagentic wave, derive the jones vector ans show the normalisation...
3. Derive the following formula for the complex Fourier Series rep- resentation of a full wave rectified sine wave of unit amplitude. Remember that the period of the rectified signal is half of that of the sine wave +00 2π
(1) Using Jones Matrix for a quarter-wave plate with fast axis vertigal, find the Jones Matrix for the same quarter-wave plate with 45 degree rotation. (2) The Jones Matrix for the same quarter-wave plate with 30 degree rotation.
Problem #4 Derive the full vector electromagnetic wave equation in terms of the magnetic field valid for linear, inhomogeneous, and isotropic materials. that is Problem #5 From the results above, derive the full vector electromagnetic wave equation in terms of the magnetic field B that is valid for linear, homogeneous, and isotropic materials. From this equation, extract and calculate the speed of light in a vacuum.
1)Polar form and 11 Exponential form Hint: Localise the complex vector in the complex plane. Define the modulus r and the argument, then convert to: Polar form: z = r(cose + i sine) = rcise Exponential form z = eie
3. If Pa(b) is the projection of vector b along vector a, show algebraically (not geometrically) and that Pd (b) b-Pa(b) is perpendicular to a. Derive general expressions for Pa(b)l P (b)l
3. If Pa(b) is the projection of vector b along vector a, show algebraically (not geometrically) and that Pd (b) b-Pa(b) is perpendicular to a. Derive general expressions for Pa(b)l P (b)l
A free electron is described by the wave function:
Using the linear momentum operator, derive an expression for
the momentum of the electron. Is your answer consistent with de
Broglie's equation?
Write answers clearly on the sheet. Show all working and underline your final answer 1. A free electron is described by the wave function, *(x) = Ae ** Using the linear momentum operator, P = -ih d/dx, derive an expression for the momentum of the electron. Is your answer...
2. Use what you know about complex numbers in polar form to derive the identity sin(a + b) = sin(a) cos(b) + cos(a) sin(b)
4.) Express the result of the complex number in polar form using 4 significant digits. [show work, check with your calculator] a) 1-(14-41)](0341) b) (14-/3) j7213
11.34 1 Given a general elliptically polarized wave as per Eq. (93): (a) Show, using methods similar to those of Example 11.7, that a linearly polarized wave results when superimposing the given field and a phase- shifted field of the form: where ? is a constant. (b) Find ? in terms of ? such that the resultant wave is linearly polarized along x.
Using Maxwell's equations, derive the expression of the generic wave equation, for a perfect dielectric, and a conducting media. Hence derive the expressions for alpha and beta for a perfect dielectric, and a conducting media. alpha - attenuation constant beta - phase constant