Practice Applying Wave Interference Formulas

Practice Applying Wave Interference Formulas
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  • 0:04 Wave Interference Overview
  • 0:37 Constructive and Destructive
  • 2:16 Determine Slit Distance
  • 3:59 Determine Distance…
  • 4:27 Solve for Theta and Length
  • 5:42 Lesson Summary
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Lesson Transcript
Instructor: Laura Foist

Laura has a Masters of Science in Food Science and Human Nutrition and has taught college Science.

Wave interference can be constructive or destructive, creating light and dark spots. We can calculate the distance between light spots, the distance between a screen and slits, and the distance between slits.

Wave Interference Overview

Wave interference problems use principles from the 19th-century double-slit experiment, which demonstrated how two waves can cause constructive or destructive interference using the same two waves, depending on our view of the interaction. This interference creates light and dark bands.

We can calculate the path distance between the light points or the dark points. We can also calculate the distance necessary between two slits to create a specific angle between the slits and the light or dark spots (or the angle that will be created by a specific slit distance).

Constructive and Destructive

The light spots, or antinodal points, create a constructive point. If the distance between the start of one wave and another, or the path difference (PD), is equal to lambda, or lambda times the whole number of nodal points (represented by m), then it is a constructive point.


Constructive


The dark spots, or nodal points, are destructive points. If the PD is equal to lambda divided by 2, or lambda divided by 2 plus the whole number of nodal points (m), then it is a destructive point.


Destructive


So, if a light source has a wavelength (lambda) of 564 nanometers (nm) and the path difference is 1128 nm, will it form a light spot or a dark spot?

1128 = 564m
m = 1128 / 564
m = 2

Since m is a whole number, this is a constructive, or light, spot.

Looking at this problem from a different perspective, how far away do the two waves need to be to form the second dark spot if the first dark spot is at m = 0 and the second dark spot is at m = 1? Let's determine where this will be located:

PD = 564(1 + 0.5)
PD = 846

The second dark spot will be formed when the two waves are 846 nm away from each other.

Determine Slit Distance

When we look at the angles used in the double-slit experiment, we can come up with two right angles with an equal angle (theta). These right triangles allow us to use trigonometry to determine some information about the waves based on two equations:


Sine equation


and


Tan equation


We have already defined PD as the difference in path length of two waves, where:

  • d is the distance between the two slits
  • y is the distance between one light spot and the next (or one dark spot and the next)
  • L is the length between the slits and the screen (or where the light/dark spots are appearing)

So let's say that the distance between two slits is 1800 nm, and the 503 nm waves form a 34-degree angle with the center line. What is the path difference between these two waves, and will it be a constructive or destructive interference?

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