## Examination process

The exam takes place in one day and consists of a written (morning) and an oral (afternoon) part. There are a total of three attempts per exam. The exam starts at 9:00 am. To participate in the oral part, you must successfully complete the written part.

Anyone who does not show up for the exam without an excuse will receive an F in KOS.

## Written part

The written part lasts 2 hours and contains 4 exercises (1st for 15 points, 2nd and 3rd for 10 points and 4th for 5 points). It is therefore possible to obtain a total of 40 points, to pass the written part you must obtain at least 20 points. The examples are at the level of examples from exercises. The grading of the written part is as follows: 0-19 = F, 20 = E-, 21-24 = E, 25-28 = D, 29-32 = C, 33-36 = B, 37-40 = A.

## Oral part

You will be assigned two topics - one from the "wave part", the other from the electromagnetic part. You have ""unlimited"" time to work on it.

The emphasis is on understanding phenomena and concepts - you have to understand what you write and what actually came out at the end of the derivation. Less emphasis on memorizing technical derivations.

In case of failure in the oral part (or rejection of the grade), the written part must also be repeated.

It is the average of the marks from the written part and from each individual topic of the oral part.

Typically, the first terms are half-empty and the end terms are crowded. Terms are not inflatable in capacity.

The oral part can stretch into the late afternoon. So allow yourself enough time. Requests for "priority check-in" will not be taken into account.

A "typical topic" in scripts consists of an introductory presentation of the problem, a more or less technical derivation, and an interpretation and discussion of the results. The most important are the opening and closing "thirds", so if you are "in a hurry" to learn, prioritize them over the "middle" - i.e. by learning technical derivation.

## Exam topics

### General wave part

• Equations of motion of a system with n degrees of freedom - approximation of small oscillations
• Solution of system equations with n degrees of freedom - method of modes, normal coordinates
• Wave equation for a string - continuous limit vs. continuous description from the beginning
• Longitudinal oscillations on a string, sound waves - description of transverse and longitudinal oscillations on a string, wave equation for sound in an ideal gas, speed of sound
• Boundary and initial conditions on a string of finite length I - fixed and free end condition, initial position and velocity, oscillations of a string with fixed ends in the form of modes
• Boundary and initial conditions on a string of finite length II - fixed and free end condition, initial position and velocity, solution of the initial problem on a string
• d'Alembert's solution of the wave equation - change of coordinates, significance of the solution; emission of travelling waves - retarded time; harmonic travelling wave
• Energy of a wave on a string - energy density and energy flow, continuity equation, relations in a travelling wave
• Dispersion relation - travelling waves, phase velocity, meaning of dispersion relation, dispersion relation for waves in space, reactive medium - waveguide/plasma, total reflection
• Wave packets and uncertainty relations - time vs frequency representation of a signal, quasi-monochromatic waves, example of a wave packet, uncertainty relations
• Group velocity - 2 harmonic waves model, meaning of group velocity, case of a general wave packet, wave packet dispersion
• Wave reflections I - reflection at the end of the string and connection of two strings - reflection experiment, junction conditions, transmission and reflection coefficients
• Wave reflections II - wave reflection on a massive connection - reflection on the connection of two strings, harmonic incident wave, junction conditions, frequency-dependent complex transmission and reflection coefficients
• Reflections III - energy ratios in reflections; transmission matrix - definition, use for reflections on multiple interfaces, matrix for connecting two strings
• Waves in space - plane and spherical waves, 3D wave equation

### Electromagnetic part

• Plane EM waves as a solution to Maxwell's equations
• Emission of an EM wave by a moving charge - connection of the field of a static and uniformly moving charge, properties of the radiation field, generalization for general motion
• Energy quantities in EM wave I - energy density and energy flow, plane wave case, Larmor's formula
• Energy quantities in EM wave II - momentum density, plane wave case, radiation pressure
• Refractive index in matter and plasma - model of EM wave interaction with matter, transparent and reactive mode, transition to the case of plasma
• Waveguide - rectangular waveguide, perfectly conducting walls, modes in the waveguide, reactive mode
• Junction conditions for the EM field at the interface of non-conductive media
• Description of polarization - general and special polarization, wave intensity, Jones vectors
• Polarization change - polarizer and wave plate, Malus law, Jones calculus
• Measuring polarization and unpolarized light - set of 4 intensities, time scales and polarization change, Stokes parameters
• The EM wave reflection at a planar interface - role of reflection, law of reflection and refraction, critical angle
• Fresnel formulas - junction conditions, 2 polarizations, definition of coefficients R and P, Brewster's angle and polarization by reflection
• Interference and the effect of temporal and spatial coherence on its visibility
• Babinet's principle - diffraction problem, perfect obstruction, complementary obstructions, Huygens-Fresnel principle
• Fraunhofer diffraction - diffraction problem, Huygens-Fresnel principle and diffraction integral, Fraunhofer diffraction integral, Fraunhofer diffraction criterion
• Application of the Fraunhofer integral - Fraunhofer integral and comparison of results for Young's experiment, diffraction grating, rectangular and circular aperture
• The effect of coherence on the visibility of the diffraction pattern - temporal and spatial coherence, the effect of a non-point light source