physics-class-12-unit-11-chapter-05-what-is-light-ii-l-5-5-3tysoerso40

### <Success style="font-size:25px"> What Is Light Ii L-5 </Success>
### <primary style="font-size:24px"> What is Light </primary>
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- **Part 2:** Electromagnetic Nature of Lightwaves & The Light Quantum

- Photograph on the right adapted from: A. Rose, _Quantum Effects in Human Vision_, Advances in Biological and Medical Physics, Vol. V, Academic Press, 1957

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<footer style = "font-size: 18px"> $\rightarrow$ What is Light $\rightarrow$ <span style = "color:blue"> What is Light </span> $\rightarrow$ Light as a Wave $\rightarrow$ Faraday's Law </footer>

### <Success style="font-size:25px"> What Is Light Ii L-5 </Success>
### <primary style="font-size:24px"> Light as a Wave </primary>
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- **Light was a wave but how could it propagate through vacuum??**

- Animation by Mr Wee Loo Kang Lawrence and Mr Fu-kwun Hwang, author of EJSS 5.0 Francisco Esquembre; used with their kind permission.

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<footer style = "font-size: 18px">What is Light $\rightarrow$ What is Light $\rightarrow$ <span style = "color:blue"> Light as a Wave </span> $\rightarrow$ Faraday's Law $\rightarrow$ Ampere's Law </footer>

### <Success style="font-size:25px"> What Is Light Ii L-5 </Success>
### <primary style="font-size:24px"> Magnetic Permeability </primary>
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- In free space

- ${E}(z, t)=\hat{\mathbf{x}} E_0 \sin (k z-\omega t)$

- ${H}(z, t)=\hat{\mathbf{y}} \sqrt{\frac{\mu_0}{\varepsilon_0}} E_0 \sin (k z-\omega t)$

- $\varepsilon_0=8.8542 \ldots \times 10^{-12} C^2 N^{-1} m^{-2}$

- dielectric permittivity of free space

- $\mu_0=4 \pi \times 10^{-7} Ns^2 C^{-2}$

- magnetic permeability of free space

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<footer style = "font-size: 18px">Maxwells Equations $\rightarrow$ Maxwells Equations $\rightarrow$ <span style = "color:blue"> Magnetic Permeability </span> $\rightarrow$ Electromagnetic Wave $\rightarrow$ Electromagnetic Wave </footer>

### <Success style="font-size:25px"> What Is Light Ii L-5 </Success>
### <primary style="font-size:24px"> Electromagnetic Wave </primary>
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- Around 1864 Maxwell predicted the existence of electromagnetic wave

- $\mathbf{E}(z, t)=\hat{\mathbf{x}} E_0 \sin (k z-\omega t)$

- $\mathbf{H}(z, t)=\hat{\mathbf{y}} \sqrt{\frac{\mu_0}{\varepsilon_0}} E_0 \sin (k z-\omega t)$

- $c=\frac{\omega}{k}=\frac{1}{\sqrt{\mu_0 \varepsilon_0}} \approx 3 \times 10^8 m/s$

- Maxwell said that

- _"light itself is an electromagnetic wave"_

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<footer style = "font-size: 18px">Maxwells Equations $\rightarrow$ Magnetic Permeability $\rightarrow$ <span style = "color:blue"> Electromagnetic Wave </span> $\rightarrow$ Electromagnetic Wave $\rightarrow$ Electromagnetic Spectrum </footer>

### <Success style="font-size:25px"> What Is Light Ii L-5 </Success>
### <primary style="font-size:24px"> Polarized Wave </primary>
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- **x - polarized wave**

- $E_x(z, t)=E_0 \cos (k z-\omega t)$

- $E_y(z, t)=0$

- **y - polarized wave**

- $E_x(z, t)=0$

- $E_y(z, t)=E_0 \cos (k z-\omega t)$

- $E_x=E_0 \sin (k z-\omega t)$

- $E_y$ = 0 and $E_z$ = 0

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<footer style = "font-size: 18px">Electromagnetic Spectrum $\rightarrow$ Maxwell's Theory $\rightarrow$ <span style = "color:blue"> Polarized Wave </span> $\rightarrow$ Unpolarized Wave $\rightarrow$ Polaroids </footer>

### <Success style="font-size:25px"> What Is Light Ii L-5 </Success>
### <primary style="font-size:24px"> Unpolarized Wave </primary>
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- For an unpolarized wave propagating in the +z-direction, the electric vector (which lies in the x-y plane) continues to change its direction in a random manner. If an unpolarized light beam is allowed to fall on a Polaroid, then the emerging beam will be x-polarized. If we place another Polaroid $P_2$, then the intensity of the transmitted light will vary as $I_0 \cos^2 \theta$.

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<footer style = "font-size: 18px">Maxwell's Theory $\rightarrow$ Polarized Wave $\rightarrow$ <span style = "color:blue"> Unpolarized Wave </span> $\rightarrow$ Polaroids $\rightarrow$ Double Refraction in Calcite </footer>

### <Success style="font-size:25px"> What Is Light Ii L-5 </Success>
### <primary style="font-size:24px"> Polaroids </primary>
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- Actual photographs with two Polaroids at different angles of relative orientation. (a) If the two Polaroids are parallel to each other, almost the entire light passes through.

- (b) when the two Polaroids are oriented at with respect to each other about 50% of the light passes through; this is because.

- (c) when the two Polaroids are at right angles to each other (notice the position of the blue dot) almost no light will pass through. Photographs courtesy: Dr. Alan J. Reed.

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<footer style = "font-size: 18px">Polarized Wave $\rightarrow$ Unpolarized Wave $\rightarrow$ <span style = "color:blue"> Polaroids </span> $\rightarrow$ Double Refraction in Calcite $\rightarrow$ Double Refraction in Calcite </footer>

### <Success style="font-size:25px"> What Is Light Ii L-5 </Success>
### <primary style="font-size:24px"> Double Refraction in Calcite </primary>
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- Photograph courtesy Professor V Lakshminarayanan and adapted from G. Ropars, A. Le Flocha and V. Lakshminarayanan, The sunstone and polarised skylight: ancient Viking navigational tools ?

- Contemporary Physics (2014).

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<footer style = "font-size: 18px">Unpolarized Wave $\rightarrow$ Polaroids $\rightarrow$ <span style = "color:blue"> Double Refraction in Calcite </span> $\rightarrow$ Double Refraction in Calcite $\rightarrow$ Einstein's Theory </footer>

### <Success style="font-size:25px"> What Is Light Ii L-5 </Success>
### <primary style="font-size:24px"> Double Refraction in Calcite </primary>
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- When an unpolarized light beam is incident normally on a calcite crystal, it usually splits up into two linearly polarized keams.
- Photograph courtesy Professor V Lakshminarayanan and adapted from G. Ropars, A. Le Flocha and V. Lakshminarayanan, The sunstone and polarised skylight: ancient Viking navigational tools ?

- Contemporary Physics (2014).

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<footer style = "font-size: 18px">Polaroids $\rightarrow$ Double Refraction in Calcite $\rightarrow$ <span style = "color:blue"> Double Refraction in Calcite </span> $\rightarrow$ Einstein's Theory $\rightarrow$ Photoelectric Effect </footer>

### <Success style="font-size:25px"> What Is Light Ii L-5 </Success>
### <primary style="font-size:24px"> Einstein's Theory </primary>
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- 1905 was Einstein's Year of Miracles; in that year, he published 5 outstanding papers .. And in one of them he said

- _... radiation energy consists of indivisible quanta of energy ...._

- E = hv

- _..that radiation must, therefore, possess a kind of molecular structure in energy, which of course contradicts Maxwell's theory._

- Wolfgang Pauli later said that this was

- _one of the landmarks in the development of theoretical physics._

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<footer style = "font-size: 18px">Double Refraction in Calcite $\rightarrow$ Double Refraction in Calcite $\rightarrow$ <span style = "color:blue"> Einstein's Theory </span> $\rightarrow$ Photoelectric Effect $\rightarrow$ Photoelectric Effect </footer>

### <Success style="font-size:25px"> What Is Light Ii L-5 </Success>
### <primary style="font-size:24px"> Photoelectric Effect </primary>
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- $T_{max}$ = hv - B Einstein Equation

- The variation of the maximum kinetic energy of the electrons as a function of frequency of the incident light.

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<footer style = "font-size: 18px">Double Refraction in Calcite $\rightarrow$ Einstein's Theory $\rightarrow$ <span style = "color:blue"> Photoelectric Effect </span> $\rightarrow$ Photoelectric Effect $\rightarrow$ Polaroid </footer>

### <Success style="font-size:25px"> What Is Light Ii L-5 </Success>
### <primary style="font-size:24px"> Polaroid </primary>
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- The probability that the polarized photon (coming out of the polaroid $P_1$ whose pass axis makes an angle $\theta$ with the x-axis) will pass through the second polaroid $P_2$ (whose pass axis is along the x-axis) is $\cos^2 \theta$.

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<footer style = "font-size: 18px">Photoelectric Effect $\rightarrow$ Photoelectric Effect $\rightarrow$ <span style = "color:blue"> Polaroid </span> $\rightarrow$ Photoelectric Effect $\rightarrow$ Photoelectric Effect </footer>

### <Success style="font-size:25px"> What Is Light Ii L-5 </Success>
### <primary style="font-size:24px"> Photoelectric Effect </primary>
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- $T_{max}$ = hv - B Einstein Equation

- Robert Millikan received the 1923 Nobel Prize in Physics _"for his work on the elementary charge of electricity and on the photoelectric effect"._

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<footer style = "font-size: 18px">Polaroid $\rightarrow$ Photoelectric Effect $\rightarrow$ <span style = "color:blue"> Photoelectric Effect </span> $\rightarrow$ Photoelectric Effect $\rightarrow$ Energy of a Photon </footer>

### <Success style="font-size:25px"> What Is Light Ii L-5 </Success>
### <primary style="font-size:24px"> Photoelectric Effect </primary>
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- E = hv' & $p=\frac{hv'}{c}$

- E = hv &  $p=\frac{hv}{c}$

- $\delta \lambda=\lambda^{\prime}-\lambda=(\frac{c}{v^{\prime}}-\frac{c}{v})=\frac{2h}{m_0c} \sin^2 \frac{\phi}{2}$

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<footer style = "font-size: 18px">Photoelectric Effect $\rightarrow$ Photoelectric Effect $\rightarrow$ <span style = "color:blue"> Photoelectric Effect </span> $\rightarrow$ Energy of a Photon $\rightarrow$ Compton Effect </footer>

### <Success style="font-size:25px"> What Is Light Ii L-5 </Success>
### <primary style="font-size:24px"> Compton Effect </primary>
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- Arthur Compton received the 1927 Nobel Prize in Physics _"for his discovery of the Compton effect"_

- In 1926, Gilbert Lewis, an American chemist, coined the word photon to describe Einstein's _localized energy quanta._

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<footer style = "font-size: 18px">Photoelectric Effect $\rightarrow$ Energy of a Photon $\rightarrow$ <span style = "color:blue"> Compton Effect </span> $\rightarrow$ Example $\rightarrow$ Photons </footer>

### <Success style="font-size:25px"> What Is Light Ii L-5 </Success>
### <primary style="font-size:24px"> Example </primary>
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- The number of photons emitted by a 50W sodium lamp in 1 second will be

- $\frac{50 W}{h v} =\frac{50 Js^{-1}}{(6.6 \times 10^{-34} Js) \times(5 \times 10^{14} s^{-1})}$

- $\approx 1.5 \times 10^{20}$ photons per second

- If a 50W sodium lamp is placed at a distance of 10 m from a circular hole of 0.1 mm radius then about 40 million photons per second will come out of the circular hole.

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<footer style = "font-size: 18px">Energy of a Photon $\rightarrow$ Compton Effect $\rightarrow$ <span style = "color:blue"> Example </span> $\rightarrow$ Photons $\rightarrow$ Polarized Photon </footer>

### <Success style="font-size:25px"> What Is Light Ii L-5 </Success>
### <primary style="font-size:24px"> Polarized Photon </primary>
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- The probability that the polarized photon (coming out of the polaroid $P_1$ whose pass axis is along the x-axis) will pass through the second polaroid $P_2$ (whose pass axis makes an angle $\theta$ with the x-axis is along the x-axis) is $\cos^2 \theta$. If the experiment is conducted with N photons (and if N is very large) then about $N \cos^2 \theta$ photons will pass through; one cannot predict the fate of an individual photon.

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<footer style = "font-size: 18px">Example $\rightarrow$ Photons $\rightarrow$ <span style = "color:blue"> Polarized Photon </span> $\rightarrow$ Polarized Photon $\rightarrow$ Quantum Random Number Generator(QRNG) </footer>

### <Success style="font-size:25px"> What Is Light Ii L-5 </Success>
### <primary style="font-size:24px"> Quantum Random Number Generator(QRNG) </primary>
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- 11110110101001010110111100110011101011111110010110

- 11001010110001000010010001100001110100101011101001

- 10010011091101101010101000100110001011010111101101

- 00011001011100001100101001100001010110001110010100

- 11011011101101000011001101011010011111100010010101

- 10100010000100001001010101000001100000010100110110

- 01011001000101100010100100010101

- Because of the indeterministic nature of quantum mechanics, we can generate true random numbers; such a device is known as quantum random number generator(QRNG).

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<footer style = "font-size: 18px">Polarized Photon $\rightarrow$ Polarized Photon $\rightarrow$ <span style = "color:blue"> Quantum Random Number Generator(QRNG) </span> $\rightarrow$ Quantis $\rightarrow$ Quantis </footer>

### <Success style="font-size:25px"> What Is Light Ii L-5 </Success>
### <primary style="font-size:24px"> Quantis </primary>
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- **An advertisement from a company selling Quantum Random Number Generators.**

- **QUANTIS** is a **random number generator** exploiting an elementary quantum optics process. Photons are sent one by one onto a semi-transparent mirror and detected. The exclusive events (reflection - transmission) are associated to "0" - "1" bit values.

- **PRODUCTS**
- True Random
 
- Number

- Generators (TRNG)

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<footer style = "font-size: 18px">Polarized Photon $\rightarrow$ Quantum Random Number Generator(QRNG) $\rightarrow$ <span style = "color:blue"> Quantis </span> $\rightarrow$ Quantis $\rightarrow$ Louis De Broglie Wrote </footer>

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### <primary style="font-size:24px"> Momentum of a Photon </primary>
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- $m v r=\frac{n h}{2 \pi} \Rightarrow 2 \pi r=\frac{n h}{m v}=n \frac{h}{p}$

- $2 \pi r=n \lambda$

- $2\pi r = n\lambda$

- $2\pi r = 6\lambda$

- $\lambda=\frac{h}{p}$ is valid for electrons, protons, photons,..

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<footer style = "font-size: 18px">Louis De Broglie Wrote $\rightarrow$ Momentum of a Photon $\rightarrow$ <span style = "color:blue"> Momentum of a Photon </span> $\rightarrow$ Wave Nature of Electrons $\rightarrow$ Electron Wave or Particle </footer>

### <Success style="font-size:25px"> What Is Light Ii L-5 </Success>
### <primary style="font-size:24px"> Wave Nature of Electrons </primary>
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- The diffraction pattern of aluminum foil produced (a) by X-rays and (b) by electrens; notice the similarity in the diffraction patterns.

- Louis De Broglie received the 1927 Nobel Prize in Physics _"for his discovery of the wave nature of electrons"._

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<footer style = "font-size: 18px">Momentum of a Photon $\rightarrow$ Momentum of a Photon $\rightarrow$ <span style = "color:blue"> Wave Nature of Electrons </span> $\rightarrow$ Electron Wave or Particle $\rightarrow$ Electron Wave or Particle </footer>

### <Success style="font-size:25px"> What Is Light Ii L-5 </Success>
### <primary style="font-size:24px"> Electron Wave or Particle </primary>
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- Is the electron (or a proton) a wave or a particle?

- $\Psi \$

- $\begin{gathered}\ i \hbar \frac{\partial \Psi}{\partial t}=H \Psi\end{gathered}$

- _Where did we get that [equation] from? Nowhere. It is not possible to derive it from anything you know._

- _It came out of the mind of Schrodinger_

- **Richard Feynman**

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<footer style = "font-size: 18px">Momentum of a Photon $\rightarrow$ Wave Nature of Electrons $\rightarrow$ <span style = "color:blue"> Electron Wave or Particle </span> $\rightarrow$ Electron Wave or Particle $\rightarrow$ Propagation of a free particle </footer>

### <Success style="font-size:25px"> What Is Light Ii L-5 </Success>
### <primary style="font-size:24px"> Propagation of a free particle </primary>
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<footer style = "font-size: 18px">Electron Wave or Particle $\rightarrow$ Propagation of a free particle $\rightarrow$ <span style = "color:blue"> Propagation of a free particle </span> $\rightarrow$ Electron Interference $\rightarrow$ Interference Pattern </footer>

### <Success style="font-size:25px"> What Is Light Ii L-5 </Success>
### <primary style="font-size:24px"> Electron Interference </primary>
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- $I=I_0 \frac{\sin^2 \beta}{\beta^2}$

- where

- $\beta=\frac{\pi b \sin \theta}{\lambda}$

- $P(p_x) d p_x=\frac{b}{\pi h} \frac{\sin^2 \beta}{\beta^2} d p_x$

- where

- $\beta=\frac{\pi b p_x}{h}=\frac{\pi b p \sin \theta}{h}=\frac{\pi b \sin \theta}{\lambda}$

- Interference experiment with electrons

- [Adapted from Feynman Lectures in Physics Vol. III].

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<footer style = "font-size: 18px">Propagation of a free particle $\rightarrow$ Propagation of a free particle $\rightarrow$ <span style = "color:blue"> Electron Interference </span> $\rightarrow$ Interference Pattern $\rightarrow$ Thank You </footer>

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<h3 id="primary-stylefont-size24px-electron-interference-primary"><primary style="font-size:24px"> Electron Interference </primary></h3>
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<p>Buildup of the electron interference pattern.</p>
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<p>Number of electrons in (a), (b), (c), (d) and (e) are 10, 100, 3000. 20000 and 70000 respectively.</p>
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<p>[Adapted from Tonomura etal., Demonstration of single electron build up of an interference pattern.</p>
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<hr>
<footer style = "font-size: 18px">Propagation of a free particle $\rightarrow$ Propagation of a free particle $\rightarrow$ <span style = "color:blue"> Electron Interference </span> $\rightarrow$ Interference Pattern $\rightarrow$ Thank You </footer>

### <Success style="font-size:25px"> What Is Light Ii L-5 </Success>
### <primary style="font-size:24px"> Interference Pattern </primary>
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- The fullerene molecule C60 consisting of 60 carbon atoms to form the smallest natural soccer ball

- Interference pattern produced by C-60 atoms Ref:: Nairz, Arndt & Zelinger Am. J Phys. Vol 71. April 2003

- The most fundamental theory now available is probabilistic in form, and not deterministic

- David Bohm was widely considered one of the best quantum physicists of all time.

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<footer style = "font-size: 18px">Propagation of a free particle $\rightarrow$ Electron Interference $\rightarrow$ <span style = "color:blue"> Interference Pattern </span> $\rightarrow$ Thank You $\rightarrow$  </footer>