physics-class-12-unit-10-chapter-01-optics-wave-optics-huygens-principle-l-1-9-onzhgk-lu00

### <Success style="font-size:25px"> Optics Wave Optics Huygens Principle L-1 </Success>
### <primary style="font-size:24px"> Diffraction and Polarisation </primary>
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- **Diffraction**

- Single slit diffraction

- Diffraction by a circular aparture

- Resolving power of optical instruments

- **Polarisation**

- Polarisation by Reflection

- Brewster Angle

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<footer style = "font-size: 18px">Wave Optics-Huygens Principle $\rightarrow$ Huygens Principle and Interference $\rightarrow$ <span style = "color:blue"> Diffraction and Polarisation </span> $\rightarrow$ Some Historical Milestones $\rightarrow$ Plane Wave </footer>

### <Success style="font-size:25px"> Optics Wave Optics Huygens Principle L-1 </Success>
### <primary style="font-size:24px"> Some Historical Milestones </primary>
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- 1621 - Snell's Law (Empirical relation)

- 1637 - Explanation of Snell's law by Descartes based on a "<span style="color:green">Corpuscular model of light,</span>" later established by Newton.

- 1678 - Huygens put forward the "<span style="color:green">Wave Theory</span>", but "<span style="color:green">corpuscular theory</span>" prevailed.

- 1801 - Young interference experiment.
* Convincing experimental evidence that "<span style="color:green">light is a wave</span>".

- 1864 - Maxwell's Theory of Electromagnetic Waves.

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<footer style = "font-size: 18px">Huygens Principle and Interference $\rightarrow$ Diffraction and Polarisation $\rightarrow$ <span style = "color:blue"> Some Historical Milestones </span> $\rightarrow$ Plane Wave $\rightarrow$ Plane Wave </footer>

### <Success style="font-size:25px"> Optics Wave Optics Huygens Principle L-1 </Success>
### <primary style="font-size:24px"> Plane Wave </primary>
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- $\psi(x, t)=A \cos (k x-\omega t)$

- $k=\frac{2 \pi}{\lambda}, \omega=2 \pi \nu$

- At any instant $t=t_1$, "<span style="color:blue">surface of constant phase</span>".

- $\left(k x-\omega t_1\right)=$ constant $\Rightarrow k x=$ constant

- $\Rightarrow x=$ constant.

- i.e. planes perpendicular to the $x$-axis.

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<footer style = "font-size: 18px">Diffraction and Polarisation $\rightarrow$ Some Historical Milestones $\rightarrow$ <span style = "color:blue"> Plane Wave </span> $\rightarrow$ Plane Wave $\rightarrow$ Plane Waves </footer>

### <Success style="font-size:25px"> Optics Wave Optics Huygens Principle L-1 </Success>
### <primary style="font-size:24px"> Plane Wave </primary>
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- As t increases x has to increase, for a given "<span style="color:blue">wave front</span>".

- $k$ is the "<span style="color:blue">propagation constant</span>" or" <span style="color:blue">phase constant</span>".

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<footer style = "font-size: 18px">Some Historical Milestones $\rightarrow$ Plane Wave $\rightarrow$ <span style = "color:blue"> Plane Wave </span> $\rightarrow$ Plane Waves $\rightarrow$ Plane Waves </footer>

### <Success style="font-size:25px"> Optics Wave Optics Huygens Principle L-1 </Success>
### <primary style="font-size:24px"> Plane Waves </primary>
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- <span style="color:blue">Propagating in an arbitrary direction</span>

* $ \psi=A \cos (\vec{k} \cdot \vec{r}-\omega t) $
* $ \vec{k}= \hat{i} k_x+ \hat{j} k_y+ \hat{k} k_z $
* $ \vec{r}=\hat{i} x+\hat{j} y+\hat{k} z $
* $ \vec{k} \cdot \vec{r}=k_x x+k_y y+k_z z $
* $ \left(\vec{k} \cdot \vec{r}-\omega t_1\right)$= constant

- $ \Rightarrow \vec{k} \cdot \vec{r}$ = constant

- $ \Rightarrow k_x x+k_y y+k_z z$ = constant

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<footer style = "font-size: 18px">Plane Wave $\rightarrow$ Plane Wave $\rightarrow$ <span style = "color:blue"> Plane Waves </span> $\rightarrow$ Plane Waves $\rightarrow$ Spherical Wave </footer>

### <Success style="font-size:25px"> Optics Wave Optics Huygens Principle L-1 </Success>
### <primary style="font-size:24px"> Plane Waves </primary>
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- <span style="color:blue">Propagating in an arbitrary direction</span>

- $\vec{k}$ is perpendicular to the planes.

- Its direction represents direction of propagation of wave, $|\vec{k}|=(2 \pi / \lambda)$ is the propagation constant.

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<footer style = "font-size: 18px">Plane Wave $\rightarrow$ Plane Waves $\rightarrow$ <span style = "color:blue"> Plane Waves </span> $\rightarrow$ Spherical Wave $\rightarrow$ Huygens Principle </footer>

### <Success style="font-size:25px"> Optics Wave Optics Huygens Principle L-1 </Success>
### <primary style="font-size:24px"> Spherical Wave </primary>
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- $\psi(r, t)=\frac{A}{r} \cos (k r-\omega t)$

- Surface of constant phase, $k r$ = constant
 
- $\Rightarrow r$ =  constant, represents surface of a sphere of radius.

- As t increases r increases, for a given wave front.

- $\frac{A}{r}$ takes care of the decrease in Intensity.

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<footer style = "font-size: 18px">Plane Waves $\rightarrow$ Plane Waves $\rightarrow$ <span style = "color:blue"> Spherical Wave </span> $\rightarrow$ Huygens Principle $\rightarrow$ Propagation of Plane Waves </footer>

### <Success style="font-size:25px"> Optics Wave Optics Huygens Principle L-1 </Success>
### <primary style="font-size:24px"> Huygens Principle </primary>
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- All points on a wavefront act like point sources that give out secondary wavelets, which propagate outward with the speed of the wave.

- The wavefront at a later time $\Delta t$ is given by the surface. tangent to these secondary wavelets.

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<footer style = "font-size: 18px">Plane Waves $\rightarrow$ Spherical Wave $\rightarrow$ <span style = "color:blue"> Huygens Principle </span> $\rightarrow$ Propagation of Plane Waves $\rightarrow$ Propagation of Plane Waves </footer>

### <Success style="font-size:25px"> Optics Wave Optics Huygens Principle L-1 </Success>
### <primary style="font-size:24px"> Propagation of Plane Waves </primary>
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- **Using Huygens Principle**

- **PLANE WAVES**

- "The new wavefront at a later time $\Delta t$ is the envelop tangent to all the secondary wavelets".

- Amplitude of the wave at the tangent only.

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<footer style = "font-size: 18px">Huygens Principle $\rightarrow$ Propagation of Plane Waves $\rightarrow$ <span style = "color:blue"> Propagation of Plane Waves </span> $\rightarrow$ Propagation of a Spherical Wave $\rightarrow$ Spherical Wave </footer>

### <Success style="font-size:25px"> Optics Wave Optics Huygens Principle L-1 </Success>
### <primary style="font-size:24px"> Spherical Wave </primary>
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- **Propagation of waves - by Huygens principle**

- <span style="color:blue">"New wavefront at a later time $\Delta t$ is the envelop tangent to the secondary wavelets".</span>

- $t=t_1$

- $ t=t_1+\Delta t $

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<footer style = "font-size: 18px">Propagation of Plane Waves $\rightarrow$ Propagation of a Spherical Wave $\rightarrow$ <span style = "color:blue"> Spherical Wave </span> $\rightarrow$ Propogation of Waves $\rightarrow$ Plane Wave Incident on a Mirror </footer>

### <Success style="font-size:25px"> Optics Wave Optics Huygens Principle L-1 </Success>
### <primary style="font-size:24px"> Law of Reflection - by Huygens Principle </primary>
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- $n_2 > n_1$

- $V_2 < V_1$

- Wavefront in the second medium is tangent to all the secondary wavelets.

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<footer style = "font-size: 18px">Plane Wave Incident on a Mirror $\rightarrow$ Relection by mirror - Huygen's principle $\rightarrow$ <span style = "color:blue"> Law of Reflection - by Huygens Principle </span> $\rightarrow$ Law of Refraction - by Huygens Principle $\rightarrow$ Application of Huygens Principle </footer>

### <Success style="font-size:25px"> Optics Wave Optics Huygens Principle L-1 </Success>
### <primary style="font-size:24px"> Law of Refraction - by Huygens Principle </primary>
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- $ B C=v_1 \Delta t $

- $ A D =v_2 \Delta t$

- In $\Delta A B C, \quad \sin i=\frac{B C}{A C}=\frac{v_1 \Delta t}{A C}$

- In $\Delta A D C, \sin r=\frac{A D}{A C}=\frac{v_2 \Delta t}{A C}$

- $\frac{\sin i}{\sin r} = \frac{v_1}{v_2} = \frac{n_2}{n_1}$(Snell's law)

- Law of refraction.

- $v_2 < v_1$ if $n_2 > n_1$

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<footer style = "font-size: 18px">Relection by mirror - Huygen's principle $\rightarrow$ Law of Reflection - by Huygens Principle $\rightarrow$ <span style = "color:blue"> Law of Refraction - by Huygens Principle </span> $\rightarrow$ Application of Huygens Principle $\rightarrow$ Huygens Secondary Wavelets at An Aperture </footer>

### <Success style="font-size:25px"> Optics Wave Optics Huygens Principle L-1 </Success>
### <primary style="font-size:24px"> Application of Huygens Principle </primary>
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- **Application of Huygens Principle to light passing through apertures**

- Plane waves are incident on this aperture.

- Rectilinear propagation of light.

- Geometrical shadow: the region where the light rays do not reach.

- Huygens principle was able to explain diffraction.

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<footer style = "font-size: 18px">Law of Reflection - by Huygens Principle $\rightarrow$ Law of Refraction - by Huygens Principle $\rightarrow$ <span style = "color:blue"> Application of Huygens Principle </span> $\rightarrow$ Huygens Secondary Wavelets at An Aperture $\rightarrow$ Reducing The Aperture Size </footer>

### <Success style="font-size:25px"> Optics Wave Optics Huygens Principle L-1 </Success>
### <primary style="font-size:24px"> Reducing The Aperture Size </primary>
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- We almost have spherical waves which are emanating from the holes.

- There were no experiments which could prove that light is a wave.

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<footer style = "font-size: 18px">Application of Huygens Principle $\rightarrow$ Huygens Secondary Wavelets at An Aperture $\rightarrow$ <span style = "color:blue"> Reducing The Aperture Size </span> $\rightarrow$ Huygens Secondary Wavelets From Two Holes In a Screen $\rightarrow$ Young's Double-Hole Experiment </footer>

### <Success style="font-size:25px"> Optics Wave Optics Huygens Principle L-1 </Success>
### <primary style="font-size:24px"> Huygens Secondary Wavelets From Two Holes In a Screen </primary>
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- The two points are $\pi$ difference in phase.

- The maxima and minima coinciding.

- Here is an intensity variation.

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<footer style = "font-size: 18px">Huygens Secondary Wavelets at An Aperture $\rightarrow$ Reducing The Aperture Size $\rightarrow$ <span style = "color:blue"> Huygens Secondary Wavelets From Two Holes In a Screen </span> $\rightarrow$ Young's Double-Hole Experiment $\rightarrow$ Young's Double-Hole Experiment </footer>

### <Success style="font-size:25px"> Optics Wave Optics Huygens Principle L-1 </Success>
### <primary style="font-size:24px"> Young's Double-Hole Experiment </primary>
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- First - With sunlight from a small opening in the roof.

- Then - With Sodium light.

* <span style="color:blue">The wave nature of light was convincingly demonstrated for the first time by Young' Experiment.</span>
 
- <span style="color:blue">Explained the formation of "fringes" by Wave Theory.</span>

* <span style="color:blue">Again, in 1802, he explained formation of "Newton's rings" by the Wave Theory.</span>

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<footer style = "font-size: 18px">Reducing The Aperture Size $\rightarrow$ Huygens Secondary Wavelets From Two Holes In a Screen $\rightarrow$ <span style = "color:blue"> Young's Double-Hole Experiment </span> $\rightarrow$ Young's Double-Hole Experiment $\rightarrow$ Thank You </footer>

### <Success style="font-size:25px"> Optics Wave Optics Huygens Principle L-1 </Success>
### <primary style="font-size:24px"> Young's Double-Hole Experiment </primary>
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- Sunlight from the roof.

- A bright intensity at the center.

- If you plot the intensity, you could see a bright intensity peak, a bright peak at the center here and then you saw some colours here and then there is uniform illumination far away from here.

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<footer style = "font-size: 18px">Huygens Secondary Wavelets From Two Holes In a Screen $\rightarrow$ Young's Double-Hole Experiment $\rightarrow$ <span style = "color:blue"> Young's Double-Hole Experiment </span> $\rightarrow$ Thank You $\rightarrow$  </footer>