physics-class-12-unit-10-chapter-06-diffraction-l-6-9-mopr6f24p4e

### <Success style="font-size:25px"> Diffraction L-6 </Success>
### <primary style="font-size:24px"> Diffraction of Light </primary>
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- Speading of light into the geomatric shadow of an obstacle or an aperture in the path of propagation of light

- If the beam of light is monochromatic then one can see bright and dark fringes or rings or patterns depending on the geomatry of the obstacle.

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<footer style = "font-size: 18px">Geometric Shadow of an Obstacle $\rightarrow$ Diffraction at a Straight Edge $\rightarrow$ <span style = "color:blue"> Diffraction of Light </span> $\rightarrow$ Diffraction at a Straight Edge $\rightarrow$ Diffraction at a Straight Edge </footer>

### <Success style="font-size:25px"> Diffraction L-6 </Success>
### <primary style="font-size:24px"> Diffraction at a Straight Edge </primary>
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- The beam undergoes diffraction at the straight edge at the top end of the wedge.

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<footer style = "font-size: 18px">Diffraction at a Straight Edge $\rightarrow$ Diffraction of Light $\rightarrow$ <span style = "color:blue"> Diffraction at a Straight Edge </span> $\rightarrow$ Diffraction at a Straight Edge $\rightarrow$ Single Slit Diffraction </footer>

### <Success style="font-size:25px"> Diffraction L-6 </Success>
### <primary style="font-size:24px"> Young Double Slit Experiment </primary>
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- Path difference = $(r_2 - r_1)$

- Phase difference = K $(r_2 - r_1)$

- $\delta$

- we treated $S_1$ and $S_2$ as a point source

- $I(\delta) = 4 I_0 cos^2 (\frac{\delta}{2})$

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<footer style = "font-size: 18px">Diffraction at a Straight Edge $\rightarrow$ Single Slit Diffraction $\rightarrow$ <span style = "color:blue"> Young Double Slit Experiment </span> $\rightarrow$ Young's Double-Slit Experiment $\rightarrow$ Finite Width of the Slit </footer>

### <Success style="font-size:25px"> Diffraction L-6 </Success>
### <primary style="font-size:24px"> Young's Double-Slit Experiment </primary>
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<footer style = "font-size: 18px">Single Slit Diffraction $\rightarrow$ Young Double Slit Experiment $\rightarrow$ <span style = "color:blue"> Young's Double-Slit Experiment </span> $\rightarrow$ Finite Width of the Slit $\rightarrow$ Two Types of Diffraction </footer>

### <Success style="font-size:25px"> Diffraction L-6 </Success>
### <primary style="font-size:24px"> Finite Width of the Slit </primary>
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- $\Delta = a sin \theta$

- Enlarged view when L is large

- Due to the finite width of the slit, there is a path difference between waver emanating from any two point sources in the aperture of the slit.

- The corresponding phase shift depends on $\theta$

- $\Rightarrow$ The intensity of $P$ depends on $\theta$.

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<footer style = "font-size: 18px">Young Double Slit Experiment $\rightarrow$ Young's Double-Slit Experiment $\rightarrow$ <span style = "color:blue"> Finite Width of the Slit </span> $\rightarrow$ Two Types of Diffraction $\rightarrow$ Fresnel Diffraction </footer>

### <Success style="font-size:25px"> Diffraction L-6 </Success>
### <primary style="font-size:24px"> Two Types of Diffraction </primary>
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- **1.** Fraunhofer Diffraction.

- **2.** Fresnel Diffraction If the source of light and the observation screen are at large distances from the diffraction aperture, so that the wavafronts arriving at the aperture and the screen may be considered plane, then it corresponds to Fraunhofer Diffraction.

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<footer style = "font-size: 18px">Young's Double-Slit Experiment $\rightarrow$ Finite Width of the Slit $\rightarrow$ <span style = "color:blue"> Two Types of Diffraction </span> $\rightarrow$ Fresnel Diffraction $\rightarrow$ Fraunhofer Diffraction </footer>

### <Success style="font-size:25px"> Diffraction L-6 </Success>
### <primary style="font-size:24px"> Fresnel Diffraction </primary>
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- When the separation between the Source and the diffraction aperture and/or the diffraction aperture and the observation screen are not large enough, the curvature of the wavefront must be taken into account. The plane wave approximation cannot be used in Fresnel Diffraction

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<footer style = "font-size: 18px">Finite Width of the Slit $\rightarrow$ Two Types of Diffraction $\rightarrow$ <span style = "color:blue"> Fresnel Diffraction </span> $\rightarrow$ Fraunhofer Diffraction $\rightarrow$ Practical Arrangement to Observe Fraunhofer Diffraction </footer>

### <Success style="font-size:25px"> Diffraction L-6 </Success>
### <primary style="font-size:24px"> Fraunhofer Diffraction </primary>
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- Out of all rays (ar plane mavefronts) travelling in all diractions, after diffraction at the aperture, the red coloured rays represent a set of parallel rays making an angle $\theta$ with the axis. They will focus at a point $P$.

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<footer style = "font-size: 18px">Two Types of Diffraction $\rightarrow$ Fresnel Diffraction $\rightarrow$ <span style = "color:blue"> Fraunhofer Diffraction </span> $\rightarrow$ Practical Arrangement to Observe Fraunhofer Diffraction $\rightarrow$ Intensity Distribution on the Focal Plane </footer>

### <Success style="font-size:25px"> Diffraction L-6 </Success>
### <primary style="font-size:24px"> Practical Arrangement to Observe Fraunhofer Diffraction </primary>
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<footer style = "font-size: 18px">Fresnel Diffraction $\rightarrow$ Fraunhofer Diffraction $\rightarrow$ <span style = "color:blue"> Practical Arrangement to Observe Fraunhofer Diffraction </span> $\rightarrow$ Intensity Distribution on the Focal Plane $\rightarrow$ Practical Arrangement to Observe Fraunhofer Diffraction </footer>

### <Success style="font-size:25px"> Diffraction L-6 </Success>
### <primary style="font-size:24px"> Intensity Distribution on the Focal Plane </primary>
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- Every point $P$ on the screen corresponds to a different angle $\theta I(\theta) \equiv I(x)$.

- The lens does not introduce any additional path difference (or phase difference) among the interfersing parallel set of rays.

- Practical Arrangement to observe Fraunhofer Diffraction

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<footer style = "font-size: 18px">Fraunhofer Diffraction $\rightarrow$ Practical Arrangement to Observe Fraunhofer Diffraction $\rightarrow$ <span style = "color:blue"> Intensity Distribution on the Focal Plane </span> $\rightarrow$ Practical Arrangement to Observe Fraunhofer Diffraction $\rightarrow$ Single slit Diffraction Intensity Distribution </footer>

### <Success style="font-size:25px"> Diffraction L-6 </Success>
### <primary style="font-size:24px"> Practical Arrangement to Observe Fraunhofer Diffraction </primary>
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<footer style = "font-size: 18px">Practical Arrangement to Observe Fraunhofer Diffraction $\rightarrow$ Intensity Distribution on the Focal Plane $\rightarrow$ <span style = "color:blue"> Practical Arrangement to Observe Fraunhofer Diffraction </span> $\rightarrow$ Single slit Diffraction Intensity Distribution $\rightarrow$ Single slit Diffraction Intensity Distribution </footer>

### <Success style="font-size:25px"> Diffraction L-6 </Success>
### <primary style="font-size:24px"> Single slit Diffraction Intensity Distribution </primary>
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- $ I(\theta) = I_o \frac {sin^2 \beta}{\beta^2}$

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

- $I_0$ is the intensity for $\theta$ = 0

- i.e at the point O, on th axis

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<footer style = "font-size: 18px">Intensity Distribution on the Focal Plane $\rightarrow$ Practical Arrangement to Observe Fraunhofer Diffraction $\rightarrow$ <span style = "color:blue"> Single slit Diffraction Intensity Distribution </span> $\rightarrow$ Single slit Diffraction Intensity Distribution $\rightarrow$ Single slit Diffraction Intensity Distribution </footer>

### <Success style="font-size:25px"> Diffraction L-6 </Success>
### <primary style="font-size:24px"> Single slit Diffraction Intensity Distribution </primary>
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- $I(\theta) = I(\beta) = I_0 \frac {sin^2 \beta}{\beta^2}$

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

- $ \beta = \frac {\sin\beta}{\beta}$

- $I_{\theta=o} = I_0$

- Single slit Diffraction: Intensity Distribution

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<footer style = "font-size: 18px">Practical Arrangement to Observe Fraunhofer Diffraction $\rightarrow$ Single slit Diffraction Intensity Distribution $\rightarrow$ <span style = "color:blue"> Single slit Diffraction Intensity Distribution </span> $\rightarrow$ Single slit Diffraction Intensity Distribution $\rightarrow$ Positions of Maxima and Minima </footer>

### <Success style="font-size:25px"> Diffraction L-6 </Success>
### <primary style="font-size:24px"> Single slit Diffraction Intensity Distribution </primary>
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- $I_{\theta} = I_{\beta} = I_0 \frac {sin^2 \beta}{\beta^2}$

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

- $\beta \rightarrow 0$

- $\frac {sin \beta}{\beta} = 1$

- $ I (\theta = 0) = I_0$

- $I_0 sin^2 \beta \times \frac {1}{\beta^2}$

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<footer style = "font-size: 18px">Single slit Diffraction Intensity Distribution $\rightarrow$ Single slit Diffraction Intensity Distribution $\rightarrow$ <span style = "color:blue"> Single slit Diffraction Intensity Distribution </span> $\rightarrow$ Positions of Maxima and Minima $\rightarrow$ Positions of Maxima and Minima </footer>

### <Success style="font-size:25px"> Diffraction L-6 </Success>
### <primary style="font-size:24px"> Positions of Maxima and Minima </primary>
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- $I(\theta)=I(\beta)=I \cdot \frac{\sin ^2 \beta}{\beta^2}$

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

- Positions of Minima are given by $\sin \beta=0$, except when $\beta=0$

- $\Rightarrow \beta=m \pi, \quad m \neq 0 $

-  i e  for  a $\sin \theta=m \lambda ; \quad m= \pm 1, \pm 2, \ldots$
 
- Thus, the first intensity minimum will occur at $\theta_1=\sin ^{-1}\left(\frac{\lambda}{\alpha}\right)$

- and at $-\theta_1=-\sin ^{-1}\left(\frac{\lambda}{a}\right)$, on either side of the central maxima, at $\theta=0$.

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<footer style = "font-size: 18px">Single slit Diffraction Intensity Distribution $\rightarrow$ Single slit Diffraction Intensity Distribution $\rightarrow$ <span style = "color:blue"> Positions of Maxima and Minima </span> $\rightarrow$ Positions of Maxima and Minima $\rightarrow$ Thank You </footer>

### <Success style="font-size:25px"> Diffraction L-6 </Success>
### <primary style="font-size:24px"> Positions of Maxima and Minima </primary>
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- $ \sin \theta_{\min }=\frac{\lambda}{a} $

- $ \lambda=500 mm =5 \times 10^{-5} cm $

-  a = 1 mm

- $ \frac{\lambda}{a}=\frac{5 \times 10^{-5}}{10^{-1}}=5 \times 10^{-4} \mathrm{rad} .$

- $ \sin \theta \approx \theta $

-  a=0-1mm

- $ \sin \theta=\frac{\lambda}{a}=\frac{5 \times 10^{-5}}{10^{-2}}=5 \times 10^{-3} $

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<footer style = "font-size: 18px">Single slit Diffraction Intensity Distribution $\rightarrow$ Positions of Maxima and Minima $\rightarrow$ <span style = "color:blue"> Positions of Maxima and Minima </span> $\rightarrow$ Thank You $\rightarrow$  </footer>