1. Module 5

1.33. Page 5

Lesson 6

Module 5—Wave Theory of Light

 

Lesson Summary

 

At the start of this lesson you were asked the following essential questions:

  • What is diffraction?
  • What is an interference pattern?
  • What is the significance of Thomas Young’s experiment as it relates to the wave model of light?
  • How are diffraction patterns solved mathematically in ideal and experimental conditions?

In this lesson you learned that diffraction occurs when any wave front bends or changes direction as it passes by the sharp edge of an obstacle or through a small opening in the obstacle.

 

If light is shone through two small openings (a double slit), the diffracted waves form an interference pattern characterized by a repeating pattern of constructive and destructive interference, which is explained by assuming light has wave-like characteristics. For this reason, Thomas Young’s double-slit experiment and observed interference pattern provided supporting evidence for the wave model of light.

 

You also learned that the interference pattern is described and analyzed as follows:

  • On either side of the central antinode, or bright fringe, in the centre of the pattern, there is a dark fringe, then a bright fringe, then a dark fringe, then a bright fringe, and so on. Each fringe is given an order.

  • Double-slit diffraction patterns can be analyzed mathematically with the following two equations. The first equation is valid for a very small angle θ.

         

  • The bright fringes, or antinodes, are the location of constructive interference where the path difference for the light travelling from both slits is a whole number of wavelengths, where n = 1, 2, 3, 4, ....

  • The dark fringes, or nodes, are the location of destructive interference where the path difference is offset by a half-number of wavelengths, where n = 0.5, 1.5, 2.5, 3.5, ....

You also learned that diffraction gratings have a large number of equally spaced, parallel lines. The equations that describe a two-slit experiment are equally useful for gratings since they only rely on the spacing between any two slits, or grooves, such as those making up the track on a CD or DVD.

 

Lesson Glossary

 

antinode: the opposite of node, a point on a standing wave pattern where there is maximum displacement

 

bright fringes: regions of constructive interference along antinodal lines

 

constructive interference: occurs when two waves combine to produce a resultant wave larger than either of the original waves

 

dark fringes: regions of destructive interference along nodal lines

 

destructive interference: occurs when two waves combine to produce a resultant wave smaller than either of the original waves

 

diffraction: the bending and spreading of waves when they interact with obstacles in their path

 

diffraction grating: an optical component that has a surface covered by a regular pattern of parallel lines or grooves that are usually separated by a distance comparable to the wavelength of light

 

node: a point on a standing wave pattern where there is no displacement and it appears to be standing still

 

polarization: the production of a state in which the plane of the electric field for each electromagnetic wave occurs only in one direction