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WAVE INTERFERENCE....

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INTERFERENCE Interference patterns are a direct result of superpositioning. Antinodal and nodal lines are produced. These patterns can be enhanced using diffraction gratings, where all waves pass through each other from multiple point sources. We also learnt that the path difference for a point on a an antinodal line is always a factor of a wavelength, , whereas for a nodal line is half a wavelength, ½. Antinodal line path difference = n Nodal line path difference = n½ Where n = order 0, 1, 2, 3, …….

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**Birds eye view of 2 waves.... Red: crest meets crest**

Or trough meets trough. Constructive interference Blue: crest meets a trough and they cancel out. Destructive interference

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**Order of magnitude (m) Can be used to calculate the path difference.**

Whole numbers: antinodal lines Half numbers: nodal lines

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Path Difference 6 wavelengths 5 wavelengths

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**S1 and S2 are two coherent sources**

All points on a wavefront are in phase with one another S1 S2 Waves interfere constructively where wavefronts meet. = antinodal lines 2 Wave Intensity (Fringes) 1 n = order number Along the nodal lines, destructive interference occurs. Here antiphase wavefronts meet. 1 2 Nodal lines-out of phase by 180 deg, Antinodal lines in phase 360 deg.

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**A series of dark and bright fringes on the screen.**

Young’s Double Slits A series of dark and bright fringes on the screen. Monochromatic light, wavelength l Double slit Screen

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**Young’s Double Slit Experiment**

THIS RELIES INITIALLY ON LIGHT DIFFRACTING THROUGH EACH SLIT. Where the diffracted light overlaps, interference occurs Double slit screen Light INTERFERENCE Some fringes may be missing where there is a minimum in the diffraction pattern Diffraction

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**Wave trains AP & BP have travelled the same distance**

Assuming the sources are coherent Wave trains AP & BP have travelled the same distance (same number of l’s) A B P Hence waves arrive in-phase CONSTRUCTIVE INTERFERENCE (Bright fringe)

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Screen Slits d L d = slit separation x = fringe separation

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**LASERS EMIT COHERENT LIGHT**

Normal light sources emit photons at random, so they are not coherent. LASER LASERS EMIT COHERENT LIGHT

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Example 5: Monochromatic light from a point source illuminates two parallel, narrow slits. The centres of the slit openings are 0.80mm apart. An interference pattern forms on screen placed 2.0m away. The distance between two adjacent dark fringes is 1.2mm. Calculate the wavelength, , of the light used.

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Example 5: Monochromatic light from a point source illuminates two parallel, narrow slits. The centres of the slit openings are 0.80mm apart. An interference pattern forms on screen placed 2.0m away. The distance between two adjacent dark fringes is 1.2mm. Calculate the wavelength, , of the light used. SOLUTION: The distance to the screen (2.0m) is large compared with the fringe spacing (1.2mm). The approximation formula can be used. n = dx/L [n = 1 because the fringe spacing is being calculated] = (8.0 x 10-4 x 1.2 x 10-3) / 2.0 = 4.8 x 10-7 m

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WAVE INTERFERENCE....

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**Decide which points are Constructive interference and which are Destructive interference?**

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Interference In phase Out of phase By 180 deg (half a wavelength)

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**Youngs Double Slit Experiment**

Quantum Physics.

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**Changing slit separation**

Double slit animation.

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A student uses a laser and a double-slit apparatus to project a two-point source light interference pattern onto a whiteboard located 5.87 meters away. The distance measured between the central bright band and the fourth bright band is 8.21 cm. The slits are separated by a distance of mm. What would be the measured wavelength of light? 524 nm x10^-7

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**Changing slit separation.**

As the separation decreases, the distance between lines increases.

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Changing wavelength As the wavelength increases, the spacing between nodal and antinodal lines increases

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Path Difference PD= m λ Two point sources, 3.0 cm apart, are generating periodic waves in phase. A point on the third antinodal line of the wave pattern is 10 cm from one source and 8.0 cm from the other source. Determine the wavelength of the waves. Two point sources are generating periodic waves in phase. The wavelength of the waves is 3.0 cm. A point on a nodal line is 25 cm from one source and 20.5 cm from the other source. Determine the nodal line number. PD = 4.5cm, PD=mλ m=4.5/3 = 1.5.

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The Diffraction Grating: This is a piece of glass with tiny slits made in it to produce small point sources. A formula can be used to relate to the interference pattern produced by a particular diffraction grating. dsin = n (Where n = 0, 1, 2, 3 …….) Often N, the number of slits per metre, or slits per centimetre is given. The slit spacing d is related to N by: d = 1/N

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** AC = AB sin and AB is the grating element = d Hence d sin = n**

For light diffracted from adjacent slits to add constructively, the path difference = AC must be a whole number of wavelengths. Grating A C Monochromatic light B AC = AB sin and AB is the grating element = d Hence d sin = n d = grating element

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**DIFFRACTION GRATING WITH WHITE LIGHT**

Hence in any order red light will be more diffracted than blue. A spectrum will result Several spectra will be seen, the number depending upon the value of d Second Order maximum, n = 2 Grating First Order maximum, n = 1 White Central maximum, n = 0 First Order maximum, n = 1 Second Order maximum, n = 2 screen

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**Note that higher orders, as with 2 and 3 here, can overlap**

Note that in the spectrum produced by a prism, it is the blue light which is most deviated grating

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**Calculate the wavelength of the light.**

Example: Light from a laser passes through a diffraction grating of 2000 lines per cm. The diagram below shows the measurement made. laser 0 order 0.5m Grating 2m 2nd order Calculate the wavelength of the light. SOLUTION: Slit spacing d = 1/N = 1/200000 = 5.00 x 10-6m sin = 0.5/2 = 0.250 = 6.25 x 10-7m = dsin/n = (5.00 x 10-6 x 0.250) / 2

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**http://webphysics. ph. msstate**

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