Thomas Young’s Double Slit Experiment by Charity I. Mulig
Historical Backdrop Publication of Christian Huygen’s treatise on light (1690). He believed that there is a medium between the eye and the objects and the object does something to cause an effect in that medium.
Historical Backdrop Mid 17th century FransescoGrimaldi observed the bending of light through narrow slits
Historical Backdrop The pervading idea of the nature of light is Newton’s Corpuscular Theory (1704). This is despite the fact that he noticed interference fringes on the edges of the prism that he used.
Historical Backdrop In 1801 Thomas Young performed his 2-slit experiment. Augustin-Jean Fresnel’s biprism experiment was later conducted in support to Young’s experiment. Fresnel’s experiment to a large extent was responsible for convincing the scientific community of the wave nature of light.
Historical Backdrop In the mid 19th century James Clerk Maxwell publish his famous equations.
Electromagnetic Wave • Produced by accelerating charges • E and B are mutually perpendicular to their direction of propagation
Huygen’s Principle “The wave fronts of light waves spreading out from a point source can be regarded as the overlapped crests of tiny secondary waves – wave fronts are made up of tinier wave fronts” Drawings from Huygen’s book Treatise on Light.
Huygen’s Principle Huygen’s principle applied to reflection and refraction of wave fronts. Huygen’s principle applied to spherical and plane wave fronts.
Diffraction Simple proof of diffraction. Waves are bent at corners and edges. The smaller the opening, the greater the diffraction.
Diffraction The shadow is fuzzier when the opening is narrower.
Interference Interference patterns of overlapping waves from two vibrating sources. “…the phenomena that occurs when two or more waves overlap in the same region or space” Young’s original drawing of 2-source (pinholes) interference pattern.
Principle of Superposition “When two or more waves overlap, the resultant displacement at any point and at any instant is found by adding the instantaneous displacements that would be produced at the point by individual waves if each were present alone.”
Requirements for … Constructive Interference Destructive Interference r2 – r1 = mλ where m is an integer r2 – r1 = mλ where m is a non-whole number
Geometry of the Set-up Actual Geometry Approximate Geometry
Interference Pattern Destructive Interference Constructive Interference where m = 0, ±1, ±2, ±3,… where m = 0, ±1, ±2, ±3,…
From the geometry of the set-up But R>>d; θ is very small and we can make the assumption So that for small angles
The wavelength of the light can then be solved as INTERESTING FACT: The Young’s experiment was the first direct measurement of light
Improvements • Use of diffraction gratings instead of slits • Fresnel’s Biprism experiment
Intensity of Each Source where
Phasor Diagram for E1 and E2 • Using the following relationships: • Cosine law
Poynting Vector in Vacuum • Has a direction along the propagation of the wave since the electric and magnetic fields are perpendicular to each other • Its magnitude is equal to the energy flow per unit area per unit time through a cross-section area perpendicular to the propagation direction “The average value of the magnitude of the poynting vector at a point is called the intensity of the radiation.”
I for Interference Pattern “The intensity of the central bright spot is 4x that of the individual sources …but the average intensity of the whole interference pattern is just twice the intensity of the individual sources.”
Phase and Path Differences • Where • k is the wave number in the material • ko is the wave number in the material • n is the index of refraction • λ is the wavelength of light in the material • λo is the wavelength of light in vacuum
Phase and Path Differences Intensity far from two sources
Bonus!!! Question: What then? Answer: • Experiment on electron interference. • De Broglie Wavelength • Davisson-Germer Experiment • Duality of Nature • Heisenberg’s Uncertainty Principle
Final Trivia Thomas Young read fluently at the age of 2; by 4, he had read the Bible twice; by 14, he knew eight languages. In adult life, he was a physician and scientist, contributing to an understanding of fluids, work and energy, and elastic properties of materials. He was the first person to make progress in deciphering Egyptian hieroglyphics. No doubt about it – Thomas Young was a bright guy!
Sources • University Physics by Young and Freedman • Fundamental Physics by Resnick • Conceptual Physics by Hewitt • Beautiful Science: http://www.huntington.org/exhibitions/beautifulscience/timelines/light_web.html • Maths.TCD : http://www.maths.tcd.ie/pub/HistMath/People/Huygens/RouseBall/RB_Huygens.html • Physics 2000: http://www.colorado.edu/physics/2000/schroedinger/electron_interference.html#evidence