Introduction To Diffraction
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Runn off worksheets.
Introduction
To understand waves, we must first comprehend the principle of superposition. The Principal of Superposition states that when two or more waves meet, the displacement of the medium is the sum of the displacements of the individual waves. The two waves behave independently, and act as vector quantities.
When two or more waves hit each other, the result is called interference. While we usually think of interference as being negative, in the case of waves it can also be positive. For example let's look at pulse X and Y in the figure below.
Fig. 1
The example above is a case of positive interference because the pulses combine to produce a larger pulse. Another name for positive interference is constructive interference.
There is a point of maximum disturbance, it is called a node. It is represented by a black dot in Fig. 1.
Below is a case of destructive interference. This interference occurs when pulses reduce or completely cancel each other out in a negative way.
In destructive interference there is a point at which minimal disturbance takes place. This is called a node. In effect, there is never a wave at this point because the pulses constantly cancel each other. If you were standing on the black dot above, you would never move up or down.
When a wave passes through a double slit, it forms two circular waves. These waves then interfere with each other producing nodes and anti nodes. See the diagram below.
If the waves that pass through the slits are light waves, then anti-nodes, or points of maximum constructive interference will be seen as bright bands, while the nodes, or points of no disturbance, will be seen as dark bands.
In order to see this interference pattern the wavelength must be constant and in phase. This means all parts of the wave are going up and down at the same time. Light of one constant wavelength is called monochromatic light. Lasers produce light that is close to monochromatic, and is in phase. Thus, if laser light is directed through a double slit pattern, it should produce dark and light lines. This pattern of bright and dark spots is called Young's interference pattern. Named after Thomas Young who first demonstrated the interference pattern.
Looking at the picture below, we can see that the bright spot in the middle of the screen is called the central bright line. The first bright band up or down is called the FIRST ORDER LINE ,the second band up or down is called the SECOND ORDER LINE, etc.
Without getting into similar right triangles and geometry, we can determine the wavelength of light with the formula
Where [[lambda]] is the wavelength of light, x is the distance between any two lines measured on the screen, d is the distance between the slits, and L is the distance between the middle of the two slits the projection screen.
The picture below shows how [[lambda]], x, d and L relate. It also shows the angle [[theta]] between the central bright line and first order line. Often it is easier to measure this angle than the actual distance between the lines.
When light passes through a single slit it produces a wide bright band flanked on either side by narrow dark bands. This occurs because at the dark band, the light arrives out of phase. Light waves interfere negatively with each other at the position of the screen and produce a dark band (anti-node). We will deal only with the first dark band. See below.
The formula that relates wavelength to length, width and diffraction pattern for a single slit is:
Where [[lambda]] is the wavelength of the light, w is the slit width, y is the distance between the middle of the bright spot and the first dark line and L is the distance between the slit and the screen.
Why is there no letter d in this formula?
A typical pattern for a single slit is shown below.
Student Objectives
* Students will identify the measurements associated with single slit diffraction.
* Students will identify the measurements associated with double slit diffraction.
* Students will solve problems associated with single slit and double slit diffraction.
Class time needed
One 50-60 minute class period
Materials
Worksheet
Pencil or pen
Calculator
Procedure
1. Read the introduction above.
2. Solve the following problems. MAKE SURE TO KEEP YOUR UNITS CONSTANT!
Problems With Solutions
Assume all light is LASER Light
1. What type of diffraction is the equation below used for? Double Slit Diffraction
Identify each of the above variables.
[[lambda]] Wavelength
x Distance between the central bright line and first order line
d Disance between the center of the two slits
L Disance between the slit plate and the screen on which the pattern is projected
sin [[Theta]] Angle between the segment running from the center of the slits to the central bright line and and the segment running from the center of the slits to the first order line.
2. What type of diffraction is the below equation used for? double slit diffraction
Identify each of the above variables.
[[lambda]] Wavelength
y Distance between central bright spot and first order dark spot
w Width of the slit
L Distance between the slit and the screen on which the pattern is projected.
3. Light falls on a double slit slide. The slits are 2.00 X 10-4 cm apart. A first-order line appears 14 cm from the central bright spot on a screen opposite the slits. The distance from the center of the slits to the first order bright line is 6.0 cm. What is the wavelength of the light.
4. Light of a wavelength of 6.0 X 10-7 m falls on a double slit slide. The slits are 2.00 X 10-4 cm apart. The distance from the center of the slits to the screen is 55 cm. How far is it from the central bright spot to the first-order line.
5. Light of a wavelength of 6.0 X 10-7 m falls on a double slit slide. The distance from the center of the slits to the screen is 55 cm and the distance from central bright spot to the first-order line is 28 cm. How far apart are the slits.
6. Light of a wavelength of 1.70 X 10-6 m falls on a double slit slide. The slits are 2.00 X 10-4 cm apart. If the distance from the central bright spot to the first-order line is 22 cm, how far are the slits from the screen?
7. Light falls on a double slit slide. The slits are 8.00 X 10-4 cm apart. A first-order line appears 14 cm from the central bright spot on a screen opposite the slits. The distance from the center of the slits to the first order bright line is 7.0 cm. What is the wavelength of the light.
8. Light of a wavelength of 9.0 X 10-7 m falls on a double slit slide. The slits are 1.85 X 10-4 cm apart. The distance from the center of the slits to the screen is 55 cm. How far is it from the central bright spot to the first-order line.
9. Light of a wavelength of 1.8 X 10-6 m falls on a double slit slide. The distance from the center of the slits to the screen is 45 cm and the distance from central bright spot to the first-order line is 28 cm. How far apart are the slits.
10. Light of a wavelength of 1.90 X 10-6 m falls on a double slit slide. The slits are 1.00 X 10-4 cm apart. If the distance from the central bright spot to the first-order line is 22 cm, how far are the slits from the screen?
11. Monochromatic light falls on a single slit 1.00 X 10-4 m wide and produces a first-order dark band 5.50 X 10-3 m from the center of the central bright band on a screen 1.00 m away. Find the wavelength of the light.
12. Monochromatic light of wavelength 9.0 X 10-7 m falls on a single slit and produces a first-order dark band of 5.50 X 10-3 m from the center of the central bright band on a screen 1.00 m away. Find the width of the slit.
13. Monochromatic light of wavelength 7.0 X 10-7 m falls on a single slit 3.00 X 10-4 m wide and produces a first-order dark band 8.50 X 10-3 m from the center of the central bright band on a screen. How far away is the screen from the slits?
14. Monochromatic light of wavelength 9.0 X 10-7 m falls on a single slit 1.00 X 10-4 m wide and produces a first-order dark band on a screen 2.00 m away. Find the distance between the central bright spot and the first-order dark band.
15. Monochromatic light falls on a single slit 2.00 X 10-4 m wide and produces a first-order dark band 8.50 X 10-3 m from the center of the central bright band on a screen 2.00 m away. Find the wavelength of the light.
16. Monochromatic light of wavelength 1.8 X 10-6 m falls on a single slit and produces a first-order dark band of 8.50 X 10-3 m from the center of the central bright band on a screen 0.50 m away. Find the width of the slit.
