Diffraction and Interference

1. Diffraction and Interference Explaining the wave nature of light.

2. Christiaan Huygens • Christiaan Huygens improvedupon the first Wave Model of Light proposed by Robert Hooke • Huygens’ Principle: A waveconsists of manysmall point sources of tinysecondarywaves, calledwavelets, whichpropogateoutward in a concentriccircleat the same speed as the waveitself. The line tangent to all the waveletsconstitutes the wave front.

3. Diffraction • Diffraction isdefined as the spreading out of the wave as it passes through a smallopening or around an obstacle • Particles do not experience diffraction • If light diffracts, thenclearlyitis a wave

4. Diffraction • Based on experimental data using water waves in a ripple tank, it has been foundthat the extent of diffraction depends on the wavelength and the width of the opening. More specifically, itdepends on the ratio of the two: • The longer the wavelength, the greater the diffraction. The smaller the opening, the greater the diffraction • Since light has a verysmallwavelenth, youneed to have a verysmallopening to experience diffraction

5. Interference

6. Interference

7. Interference

8. Young’sExperiment Bright areas on the interference pattern represent constructive interference and are called maxima and dark areas represent destructive interference and are called minima.

9. Young’sExperiment • Antinodes are defined as positions in an interference pattern where there is only constructive interference • Nodes are defined as positions in an interference pattern where there is only destructive interference

10. The Central Antinode • The central antinode occurs along the perpendicular bisector • Both waves travel the same distance from the slits to the screen and therefore arrive at the screen in phase .

11. The First Node • The first node is also called the first minimum or first dark fringe. • One wave will travel half a wavelength more than the other, causing them to be out of phase (destructive interference)

12. The First Antinode • The first antinode is also called the first maximum or first dark fringe. • One wave will travel one wavelength more than the other, causing them to be in phase (constructive interference)

13. The Mathematics • Recall that antinodes have a path difference of one wavelength • The distance S1 – X represents the path difference. • If Pnis a large distance from the slits, then the two paths are approximately parallel near the slits and as such, we can make a right triangle connecting S2 to X. • As a result of this right triangle, we have the following relationship:

14. The Mathematics • For nodes (destructive interference), we could derive the relationship the same way with one difference: the path difference is half a wavelength. • As such our formula for nodes is:

15. FindingWavelengthExperimentally • In the laboratory, it is difficult to measure the angle of diffraction because it is extremely small. • It is much easier to find sinθ by determining where l is much larger than x allowing us to use sinθ rather than tan θ

16. FindingWavelengthExperimentally • If we substitute into our relationship in place of sinθand solve for wavelength, we get a new relationship for antinodes: • and for nodes: • Remember this equation is an approximation and only suitable • for θ <10o

17. Diffraction Gratings • Young’s experiment only used two small openings. • A diffraction grating has a very large number of equally spaced, parallel lines that act as individual light sources • The pattern that is created is similar to the double slit apparatus, but delivers more energy increasing the brightness of the fringes. The fringes are also narrower. • If light with multiple wavelengths is used, a diffraction grating will separate the wavelengths and a spectrum will be produced. • Diffraction gratings usually are described in terms of number of lines per unit of measurement • Ex) 1000 lines/cm • To determine the value of d (distance between slits), find the inverse of number of lines per unit of measurement • Ex) d = 1/1000 lines/cm = 0.001 cm

18. In Summary If the angle is > 10o, the second equation must be used. It is helpful to determine the angle at the beginning of the problem in order to determine which equation is appropriate to use.

19. Example 1 Monochromatic light is incident on two slits separated by 0.30 mm, and the first bright fringe (n = 1 antinode) is located at an angle of 0.080 from the central antinode. • What is the wavelength of the light?

20. Example 2 A student measuring the wavelength of light emitted by a krypton gas sample directs the light through two slits separated by 0.264 mm. An interference pattern is created on a screen 3.0 m from the slits and the distance between the second bright (n = 2 antinode) fringe and the central antinode is measured to be 1.18 cm. • What is one of the wavelengths of light emitted by the krypton gas sample?

21. Example 3 A diffraction grating has 1000 lines/1 cm. When light passes through the grating, an interference pattern is produced on a screen 4.00 m away. The first-order bright fringe is 19.2 cm away from the central antinode. What is the wavelength and colour of the light?