2nd & 3th N.U.T.S. Workshops Gulu University Naples FEDERICO II University 6 – Interference

Soap Bubbles … and Oil Spot 2nd & 3th NUTS Workshop ( Jan 2010) Soap Bubbles … and Oil Spot What is producing so nice colours ? In every-day life several examples of coloured situations derive from the interference phenomenon of light To make soap bubbles in a low-cost way, add a small ammount of dish washing liquid to water, stir well, blow through a hollow stick and a bubble will be produced Work in a sunny area, ask the student to observe the colours on the bubble surface and to explain, in their common words, why it is so. Have them note these explanations. 6- Interference

Other Examples of Nice Coulours … 2nd & 3th NUTS Workshop ( Jan 2010) Other Examples of Nice Coulours … In every-day life several examples of coloured situations derive from the interference phenomenon of light To make soap bubbles in a low-cost way, add a small ammount of dish washing liquid to water, stir well, blow through a hollow stick and a bubble will be produced Work in a sunny area, ask the student to observe the colours on the bubble surface and to explain, in their common words, why it is so. Have them note these explanations. 6- Interference 3 3

It’s just a Phase Difference Pattern! 2nd & 3th NUTS Workshop ( Jan 2010) It’s just a Phase Difference Pattern! or a Thin Film Interference Constructive and destructive interference of light waves is the reason why thin films, such as soap bubbles, show colorful patterns. Light waves reflecting off the top surface of a film interfere with the waves reflecting from the bottom surface. To obtain a nice colored pattern, the thickness of the film has to be of the order of the wavelength of light. Variable thickness of the film give variable wavelength (colour) of the refracted light constructive interference 6- Interference

What is Interference? Combined Waveform wave 1 wave 2 2nd & 3th NUTS Workshop ( Jan 2010) What is Interference? Combined Waveform wave 1 wave 2 If two waves (same wavelength and frequency) are in phase, both wave crests and troughs align. Constructive interference results increase in the wave amplitude, for light a brightening of the waveform in that location. If the two waves are out of phase, then the crests will align with the troughs. Destructive Interference results, a decrease in the amplitude of the combined wave, for light a dimming of the waveform at that location. 6- Interference

Interference: SUPERPOSITION of 2 or more Waves in the same region 2nd & 3th NUTS Workshop ( Jan 2010) Interference: SUPERPOSITION of 2 or more Waves in the same region ONLY UNDER SPECIFIC CONDITIONS 6- Interference 6 6

Conditions to Have Interference 2nd & 3th NUTS Workshop ( Jan 2010) Conditions to Have Interference In the simplest case: Superposition of periodic waves with same frequency. The waves’ sources oscillate in phase. i.e. synchronously, or with phase difference constant and known (COHERENT SOURCES) 6- Interference

Example of Incoherent Light Source 2nd & 3th NUTS Workshop ( Jan 2010) Example of Incoherent Light Source An incandescent lamp is a good example of incoherent light source. The many small part of the filament emit light with different phases, no correlation constant in time exists amongst the emitted light bursts. To produce two coherent light sources a single source has to be used, with some apparatus capable of producing two light beams (splitting the light beam coming from the source, ex: Fresnel bi-prism) 6- Interference

Interference for Coherent Sources (longitudinal and transversal waves) 2nd & 3th NUTS Workshop ( Jan 2010) Interference for Coherent Sources (longitudinal and transversal waves) 6- Interference 9 9

The original drawing by T. Young to illustrate its experiments. 2nd & 3th NUTS Workshop ( Jan 2010) Young’s Experiment The double-slit experiment, performed by the English scientist T. Young in 1801, is an attempt to resolve the question of whether light was composed of particles (Newton's "corpuscular" theory), or rather consisted of waves. The Interference Patterns observed in the experiment seemed to discredit the corpuscular theory; the wave theory of light remained well accepted until early 20th century. The original drawing by T. Young to illustrate its experiments. 6- Interference

Double-slit Experiment: Schema 2nd & 3th NUTS Workshop ( Jan 2010) Double-slit Experiment: Schema plane waveforms to focus on the screen To have a constructive interference along the θ direction the path length difference between the wavefronts coming from the two apertures have to be an integer number of wavelengths: d sin θ= mλ 6- Interference

Another Schema of Young Experiment 2nd & 3th NUTS Workshop ( Jan 2010) Another Schema of Young Experiment 6- Interference 12 12

YOUNG Ex conditions for MAX and MIN Intensity 2nd & 3th NUTS Workshop ( Jan 2010) YOUNG Ex conditions for MAX and MIN Intensity BRIGHT FRINGE : DARK FRINGE : 6- Interference 13 13

Geometry of N-slits Interference 2nd & 3th NUTS Workshop ( Jan 2010) Geometry of N-slits Interference λ rj a x x′ L θ d 1 2 j N d = spacing between two slits L = screen distance from the plane of the slits N = total number of slits  = angle between the direction of incoming beam and the considered out coming one  = wavelength of the incident light It can be useful to become familiar with the Interference from a multiple slit system also because its knowledge helps in understanding how a diffraction grating functions 6- Interference

N-slits Interference: the Solution for I 2nd & 3th NUTS Workshop ( Jan 2010) N-slits Interference: the Solution for I Interference of red laser light 2 slits 5 slits The expression for the Intensity I is valid for any number N of slits, note the dependence on the angle, the larger the angle with respect to the normal, the weaker the intensity of the fringe The intensity of the interference pattern produced by a multiple (in this case 5 slits) is shown in the photo at the bottom, from a real experiment. The light emitted by a laser is coherent because of the feature of the laser light emission process; this can be explained in terms of atomic spectra characteristics 6- Interference

Double-slit Maxima Location 2nd & 3th NUTS Workshop ( Jan 2010) Double-slit Maxima Location Maxima  when denominator = 0 n is the fringe order - n is a positive o negative integer - there is a nmax (nmax= max integer ≤d/λ) - total number of fringes =2 nmax+1 (from -nmax to +nmax ) 6- Interference

5-slits Versus Double Slit 2nd & 3th NUTS Workshop ( Jan 2010) 5-slits Versus Double Slit Maxima 5-slit  when denominator = 0 same as 2-slit!!! only the fringe width is narrower with respect to 2-slit (the fringe width is proportional to the numerator period!) Interference of red laser light 2 slits 5 slits 6- Interference

Multi-slits Interference We Will Work on 2nd & 3th NUTS Workshop ( Jan 2010) Multi-slits Interference We Will Work on to build a low cost spectroscope 6- Interference