Foundation year General Physics PHYS 101 Lecture 14 Instructor: Sujood Alazzam 2015/2016 1

Wave properties of matter Interference Diffraction Electromagnetic spectrum X-ray Polarization

Waves origin phase , relative to origin wavelength amplitude A

The Principle of Superposition 4 When two or more waves overlap, the net disturbance at any point is the sum of the individual disturbances due to each wave.

Adding wave functions “Crystal Structure Analysis for Chemists and Biologists”, Glusker, Lewis and Rossi, VCH, 1994.

Interference  For waves with the same frequency and amplitude, we see constructive interference when two waves have a phase difference of n, where (n  ℤ ) ­called “in phase”  Destructive interference is observed for a phase difference of (n + ½), where (n  ℤ ) ­called “out of phase”  A phase difference can result from a path difference ­happens in slit experiments ­the same thing happens when X-rays are diffracted by a crystal

Diffraction A wave passing through a small opening will diffract, as shown. This means that, after the opening, there are waves traveling in directions other than the direction of the original wave.

Diffraction To investigate the diffraction of light, we consider what happens when light passes through a very narrow slit. As the figure indicates, what we see on the screen is a single-slit diffraction pattern.

The Inside Scoop on Light Light is a wave, kind of like a wave in the ocean These light waves carry energy. This energy can do many interesting things, like help grow a plant, produce electric currents, or cause chemical reactions. Light carries a different amount of energy depending on its wavelength.

Light that has a longer wavelength appears more red, and light that has a shorter wavelength appears blue. The shorter the wavelength, the higher the energy carried by the wave. You may have heard of “ultraviolet” or “infrared” light. That is light at either extreme of wavelength, very short (ultraviolet) or very long (infrared). Our eyes cannot always detect light if the wavelength is very long or very short.

Models of light light is a wave light is a particle So which one is right? They are both right...and they are both wrong. That’s called wave-particle duality In some experiments, the wave model works best. In other experiments, the particle model works best. Thus, we use both.

Light is a wave Propagating wave of oscillating electric and magnetic fields described by wavelength,, and frequency, f. f = v where v is the speed of the wave. – In a vacuum, v = c = 3.00 x 10 8 m/s. – large wavelength corresponds to small frequency and small wavelength corresponds to large frequency.

Wavelength and Frequency

Light comes in many wavelengths When white light passes through a glass prism (or a diffraction grating), it separates into colors. These colors have different wavelengths. This group of wavelengths is the visible part of the electromagnetic spectrum.

Light is a particle Albert Einstein proposed that light consisted of photons. A photon is a “particle” or “packet” of energy. A photon has an energy of E=hf where h is called Planck’s constant and f is frequency. High frequency (low wavelength) photons have high energy; low frequency (high wavelength) photons have low energy.

Light, Photons and Planck Planck’s law relates the energy of a photon to its frequency or wavelength E = energy of a photon h = Planck’s constant c = speed of light = wavelength of light The value of the constant h in this equation, called Planck’s constant, has been shown in laboratory experiments to be h = x 10 –34 J s

Wave properties of matter Material particles behave as waves with a wavelength given by the de Broglie wavelength (Planck’s constant/momentum) λ=h/p Where p is the momentum p=m v= mass *velocitY so λ=h/mv

Electromagnetic Waves

An electromagnetic wave propagating in the positive x direction, showing the electric and magnetic fields:

All electromagnetic waves propagate through a vacuum at the same rate:

The Electromagnetic Spectrum Because all electromagnetic waves have the same speed in vacuum, the relationship between the wavelength and the frequency is simple: The full range of frequencies of electromagnetic waves is called the electromagnetic spectrum.

Radio waves are the lowest-frequency electromagnetic waves that we find useful. Radio and television broadcasts are in the range of 10 6 Hz to 10 9 Hz. Microwaves are used for cooking and also for telecommunications. Microwave frequencies are from 10 9 Hz to Hz, with wavelengths from 1 mm to 30 cm.

Infrared waves are felt as heat by humans. Remote controls operate using infrared radiation. The frequencies are from Hz to 4.3 x Hz.

Visible light has a fairly narrow frequency range, from 4.3 x Hz (red) to 7.5 x Hz (violet). Ultraviolet light starts with frequencies just above those of visible light, from 7.5 x Hz to Hz. These rays cause tanning, burning, and skin cancer. Some insects can see in the ultraviolet, and some flowers have special markings that are only visible under ultraviolet light. X-rays have higher frequencies still, from Hz to Hz. They are used for medical imaging.

Gamma rays have the highest frequencies of all, above Hz. These rays are extremely energetic, and are produced in nuclear reactions. They are destructive to living cells and are therefore used to destroy cancer cells.

X-ray Production X-rays are electromagnetic radiation. X-rays are produced due to sudden deceleration of fast moving electrons when they collide and interact with the target anode. In this process of deceleration more than 99% of the electron energy is converted into heat and less than 1% of energy is converted into X-ray production.

Scattering X-rays

X-ray machines X-rays are photons, like visible light photons only with much more energy. Diagnostic x-rays are used to produce images of bones and teeth on x- ray film. X-ray film turns black when exposed to x-rays.

Therapeutic X-rays are used to destroy diseased tissue, such as cancer cells. Low levels of x-rays do not destroy cells, but high levels do.

PHY232 - Remco Zegers - interference, diffraction & polarization 30 Polarization  We saw that light is really an electromagnetic wave with electric and magnetic field vectors oscillating perpendicular to each other. In general, light is unpolarized, which means that the E-field vector (and thus the B-field vector as long as it is perpendicular to the E-field) could point in any direction propagation into screen E-vectors could point anywhere: unpolarized

PHY232 - Remco Zegers - interference, diffraction & polarization 31 Polarized light  light can be linearly polarized, which means that the E-field only oscillates in one direction (and the B-field perpendicular to that)

PHY232 - Remco Zegers - interference, diffraction & polarization 32 question  Because of reflection from sunlight of the glass window, the curtain behind the glass is hard to see. If I would wear polaroid sunglasses that allow … polarized light through, I would be able to see the curtain much better.  a) horizontally  b) vertically horizontal vertical direction of polarization of reflected light

PHY232 - Remco Zegers - interference, diffraction & polarization 33 sunglasses wearing sunglasses will help reducing glare (reflection) from flat surfaces (highway/water) withoutwith sunglasses

QUIZ Q1: true or false: Electric and magnetic fields always exist together. The fields can’t exist in a vacuum.

Cont. Radio waves have the shortest wavelengths in the electromagnetic spectrum. Microwaves have wavelengths that can be measured in nanometers! The longer microwaves, those closer to a foot (~30 cm) in length, are the waves which heat our food in a microwave oven. The heat that we feel from sunlight, a fire, a radiator or a warm sidewalk is infrared. Visible light is made up of the same frequencies of colored light.

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