Thomas Young’s Double Slit Experiment by Charity I. Mulig 1

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. 2

Historical Backdrop Mid 17 th century Fransesco Grimaldi observed the bending of light through narrow slits 3

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. 4

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. 5

Historical Backdrop In the mid 19 th century James Clerk Maxwell publish his famous equations. 6

Prerequisite Information 7

Electromagnetic Wave Produced by accelerating charges E and B are mutually perpendicular to their direction of propagation 8

Huygen’s Principle Drawings from Huygen’s book Treatise on Light. “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” 9

Huygen’s Principle Huygen’s principle applied to reflection and refraction of wave fronts. Huygen’s principle applied to spherical and plane wave fronts. 10

Diffraction Simple proof of diffraction. Waves are bent at corners and edges. The smaller the opening, the greater the diffraction. 11

Diffraction The shadow is fuzzier when the opening is narrower. 12

Interference “…the phenomena that occurs when two or more waves overlap in the same region or space” Interference patterns of overlapping waves from two vibrating sources. Young’s original drawing of 2-source (pinholes) interference pattern. 13

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.” 14

Requirements for … Constructive InterferenceDestructive Interference r 2 – r 1 = mλ where m is an integer r 2 – r 1 = mλ where m is a non-whole number 15

The Experimental Set-up 16

Geometry of the Set-up Actual GeometryApproximate Geometry 17

Interference Pattern Destructive Interference where m = 0, ±1, ±2, ±3,… Constructive Interference where m = 0, ±1, ±2, ±3,… 18

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 19

The wavelength of the light can then be solved as INTERESTING FACT: The Young’s experiment was the first direct measurement of light 20

Improvements Use of diffraction gratings instead of slits Fresnel’s Biprism experiment 21

Intensity of Interference Pattern 22

Intensity of Each Source where 23

Phasor Diagram for E 1 and E 2 Using the following relationships: Cosine law 24

Solving for E P 25

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.” 26

I for Sinusoidal Wave in a Vacuum 27

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.” 28

Phase and Path Differences Where k is the wave number in the material k o is the wave number in the material n is the index of refraction λ is the wavelength of light in the material λ o is the wavelength of light in vacuum 29

Phase and Path Differences Intensity far from two sources 30

For 2-slit interference, I may also be expressed as… 31

Bonus!!! Question: What then? Answer: 1.Experiment on electron interference. 2.De Broglie Wavelength 3.Davisson-Germer Experiment 4.Duality of Nature 5.Heisenberg’s Uncertainty Principle 32

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! 33

Sources University Physics by Young and Freedman Fundamental Physics by Resnick Conceptual Physics by Hewitt Beautiful Science: ce/timelines/light_web.html ce/timelines/light_web.html Maths.TCD : ns/RouseBall/RB_Huygens.html ns/RouseBall/RB_Huygens.html Physics 2000: on_interference.html#evidence 34