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Diffraction and Interference. Explaining the wave nature of light. Christiaan Huygens. Christiaan Huygens improved upon the first Wave Model of Light proposed by Robert Hooke
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Diffraction and Interference Explaining the wave nature of light.
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.
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
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
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.
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
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 .
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)
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)
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:
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:
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
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
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
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.
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?
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?
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?