What is a reflecting boundary condition?

The boundary condition u=0 in a wave equation reflects the wave, but u changes sign at the boundary, while the condition ux=0 reflects the wave as a mirror and preserves the sign, see a web page or a movie file for demonstration.

What are the conditions for reflection?

Following are the two conditions for the total internal reflection to take place: The angle of incidence in the denser medium must be greater than the critical angle for that pair of media. The ray of light must travel from a denser medium into a rarer medium.

What is the boundary condition for a free end reflection?

Reflection from a SOFT boundary The net vertical force at the free end must be zero. This boundary condition is mathematically equivalent to requiring that the slope of the string displacement be zero at the free end (look closely at the movie to verify that this is true).

How are waves reflected at a fixed boundary?

First the reflected pulse is inverted. That is, if an upward displaced pulse is incident towards a fixed end boundary, it will reflect and return as a downward displaced pulse. Similarly, if a downward displaced pulse is incident towards a fixed end boundary, it will reflect and return as an upward displaced pulse.

How does reflection from a hard boundary work?

Reflection from a HARD boundary. The animation at left shows a wave pulse on a string moving from left to right towards the end which is rigidly clamped. As the wave pulse approaches the fixed end, the internal restoring forces which allow the wave to propagate exert an upward force on the end of the string.

What are the boundary conditions for Region I?

In this case, the boundary conditions occur where region I meets region II (at x = 0), and where region II meets region III (at x = 18 m): Let’s check the “position” values first. Q: What is the y-position of the sum of the travelling waves at x = 0 m ? Q: What is the y-position of the sum of the travelling waves at x = 18 m ?

What happens to a reflected wave at a free boundary?

The reflected wave pulse propagates from right to left, with the same speed and amplitude as the incident wave, and with the same polarity (right-side up). at a free (soft) boundary, the restoring force is zero and the reflected wave has the same polarity (no phase change) as the incident wave.

How are EM waves related to boundary conditions?

Griffiths does waves on a string (9.1), EM waves in vacuum (9.2), EM waves in linear media (9.3), and EM waves in conductors (9.4) and for each one he (a)comes up with the wave equation, (b) finds its solutions, (c) discusses polarization states, and (d) matches boundary conditions and finds reflected and transmitted properties. I, instead,