Question

_____ is the relation bettween group velocity and beta in equation a) Vg= dw/beta b) Vg= w/beta c) Vg= wbeta d) none
​

Answer 1

Answer:

With IQ 148 you are in the group of genius or near genius. You have the ability to think extremely brilliant, and sharp in many areas. With your IQs, you can easily achieve success in one or more areas.

Answer 2

Answer:

SUPERPOSITION OF LIGHT WAVES

When we analyze the resultant of two or more simple harmonic vibrations (monochrome light waves), we usually can treat it as the simple sum of the individual vibrations (waves) as shown below.

Note:

This linear treatment is only true for low power intensity lights. When the power intensities are very high (such as with an electric field strength at 1012 volts/meter), non-linear effects will be excited and the simple sum method should not be used.

However, in this discussion, we can use the simple sum method.

SUPERPOSED WAVE OF DIFFERENT FREQUENCIES (VERY SMALL DIFFERENCE) AND BEATS

We will now discuss the superposition of two waves that have same vibration direction, same amplitude a, but different frequency and wave number(ω1, k1, ω2, k2). However, the frequency difference is very small. This will generate the very interesting “beat” phenomenon.

Since the phase difference between the vibrations is continually changing, the specification of some initial nonzero phase difference is in general not of major significance in this case.

So we can suppose that the individual vibrations have an initial phase of 0, and hence can be written as:

Then the sum of these two waves is:

Using the following triangular formula

We get

We then introduce the notation of average angular frequencyand average wave number

And modulation frequency ωm and modulation wave number km

We then get

We can make

Then we get

This means that the resultant superposed wave has an angular frequency, and its amplitude varies between 0 and 2a with time t and position z.

The following picture shows the superposition result. Since light waves have very high frequency, if ω1 ≈ ω2, then >> ωm, which means that A varies slowly but E varies extremely fast.