# Waves path and phase difference relationship goals

### Wavelength, Path Difference, Phase Difference | Physics Forums

If your slits are further apart, the light waves will be coming from spots that are further apart. That means that their path lengths will be more different from one. Path difference: It is the difference between the lengths of two paths of the two different waves having same frequency and travelling at same velocity. Phase. Objectives. When you finish Define phase angle and its relationship to a wave front. .. terms of the path difference, which we can relate to the wavelength λ.

The resulting, combined wave will have crests that are shorter than the crests of either original wave, and troughs that are shallower than either of the incoming waves. This is known as destructive interference. In fact, if the two waves with the same amplitude are shifted by exactly half a wavelength when they merge together, then the crest of one wave will match up perfectly with the trough of the other wave, and they will cancel each other out.

The resulting combined wave will have no crests or troughs at all, and will instead just look like a flat line, or no wave at all! Figure of destructive interference of two out of phase waves creating no wave Double slit interference Say you have a laser pointer.

A laser is basically just a bunch of light waves that all have the same wavelength and are all lined up with one another. Suppose you place a card in front of the laser beam with two slits in it, such that waves can only pass through two spots.

You then measure the amount of light that hits the wall on the other side of the room at various points. Figure of laser beam passing through two slits towards opposite wall For the experiment to work, the slits have to be tiny compared to the distance from the card to the wall, but they have to be larger than a single wavelength of the light.

## The Path Difference

That means that if we choose a spot on the wall, two light waves will be hitting it; one from the top slit and one from the bottom slit. As they get close to the wall, and close to one another, they will start to interfere.

Figure of waves in phase passing through slits and becoming out of phase as they near the opposite wall above the top slit The light coming from the bottom slit has to come much further than the light from the top slit, so more wavelengths will be needed to travel the longer distance. The key is to compare the number of wavelengths it takes for each light wave to travel from the slit to the wall.

For constructive interference, the difference in wavelengths will be an integer number of whole wavelengths.

## Diffraction and constructive and destructive interference

For destructive interference it will be an integer number of whole wavelengths plus a half wavelength. Think of the point exactly between the two slits. The light waves will be traveling the same distance, so they will be traveling the same number of wavelengths. That means that there will always be constructive interference at that spot, so we will always see a bright spot on the wall in the middle.

At that point, one of the waves will hit the wall with a crest when the other hits with a trough, so they will effectively cancel one another out, resulting in a dark spot there. This will result in another bright spot on the wall.

This pattern will keep alternating so that we get a pattern of light spots and dark spots, both above and below our center bright spot.

Figure of diffraction pattern on the opposite wall If your slits are further apart, the light waves will be coming from spots that are further apart. That means that their path lengths will be more different from one another, giving bright spots that are closer together. We can pretend to divide our slit into pieces, and compare the path lengths of the light coming from these pieces to one another to discover what sort of interference pattern we will get when they interact.

They are an equal distance from the center of the slit, so their path lengths to the center point on the wall will be the same. We know that that means they will interfere constructively with one another. If we choose two points that are further in, but still the same distance from the middle of the slit, they will also have equal path lengths to the center point on the wall. A representative two-point source interference pattern with accompanying order numbers m values is shown below.

In this part of Lesson 3, we will investigate the rationale behind the numbering system and develop some mathematical equations that relate the features of the pattern to the wavelength of the waves. This investigation will involve the analysis of several antinodal and nodal locations on a typical two-point source interference pattern.

It will be assumed in the discussion that the wave sources are producing waves with identical frequencies and therefore identical wavelengths. To begin, consider the pattern shown in the animation below. Point A is a point located on the first antinodal line. This specific antinode is formed as the result of the interference of a crest from Source 1 S1 meeting up with a crest from Source 2 S2.

The two wave crests are taking two different paths to the same location to constructively interfere to form the antinodal point. The crest traveling from Source 1 S1 travels a distance equivalent to 5 full waves; that is, point A is a distance of 5 wavelengths from Source 1 S1.

The crest traveling from Source 2 S2 travels a distance equivalent to 6 full waves; point A is a distance of 6 wavelengths from Source 2 S2. While the two wave crests are traveling a different distance from their sources, they meet at point A in such a way that a crest meets a crest.

### Diffraction and constructive and destructive interference (article) | Khan Academy

But will all points on the first antinodal line have a path difference equivalent to 1 wavelength? And if all points on the first antinodal line have a path difference of 1 wavelength, then will all points on the second antinodal line have a path difference of 2 wavelengths? And what about the third antinodal line? And what about the nodal lines?