Huygens' Principle and Diffraction PDF

**Huygens\' principle and diffraction** When light passes through an aperture, every point on the light wave within the aperture can be viewed as a source creating a circular wave that propagates outward from the aperture. The aperture thus creates a new wave source that propagates in the form of a...

**Huygens\' principle and diffraction** When light passes through an aperture, every point on the light wave within the aperture can be viewed as a source creating a circular wave that propagates outward from the aperture. The aperture thus creates a new wave source that propagates in the form of a circular wavefront is shown in figure 7. 7 (a) and (b). The centre of the wavefront has greater intensity while the edges have a lesser intensity is as shown in figure 7.8. This explains the observed diffraction pattern and why a perfect image of the aperture on a screen is not created. **The single slit diffraction** When light passes through a single slit whose width w is on the order of the wavelength of the light, then can be observed a single slit diffraction pattern on a screen that is a distance L \>\> w away from the slit. The intensity is a function of angle. Huygens\' principle tells us that each part of the slit can be thought of as an emitter of waves. All these waves interfere to produce the diffraction pattern. Constructive interference can be occured when two crests meet each other and destructive interference can be occured when crest meets trough. The single slit diffraction pattern of light is shown in figure 7.9. In order to study the diffraction pattern on a screen (figure 7.10), the single-slit experiment is employed. Consider a monochromatic source of light that passes through a slit width \"a\" as shown in the figure. At point P on the screen, the secondary waves interfere destructively and produce a dark fringe. Let \"D\" be the distance between the slit and the screen, and \"y\" be the distance between point P and point O, the center of the screen. AC is perpendicular to BP. Let 0 be the angle of diffraction, and 0 is the angle BAC. **Chapter 7 \| Interference, Diffraction and Polarization of Light (161)** We assume that the screen is at a considerable distance from the slit, i.e., D \>\> a. Hence, 0=0\' and, sin 0≈ tan 0≈ 0 = The path difference between the two rays AP and BP is given by, A=BP-AP = BC In the right-angled triangle BCA, *BC* sin 0\' = sin 0= *BA* BC= BA sin 0 = a sin 0 Therefore, A = a sin 0 **Diffraction Minima** The condition for minima or dark fringe is, Path difference = integral multiple of wavelength A = nλ a sin 0 = nλ *y* (n = +1, +2, +3, , etc.) a = nλ Ул *D* *nλD* a This equation gives the distance of the nth dark fringe from the center. The fringe width is given by, *2D-nλD* n *a* *a* B=y-y=(n+1) or, *ND* B = a **Diffraction Maxima** The condition for maxima or bright fringe is, Path difference = non-integral multiple of wavelength A = (n + 1/2 ) 2 (n =±1, ±2, ±3, \..., etc.) a sin 0 = (n+1)2 (162) Grade, 12 Physics *Th* in FES *TH* ie.D\>\> *dark fringe from* a -(n+1)x Yn =(n+12) AD a The intensity of single-slit diffraction is given by, 1=1, \[sin (π a sin)/( a sin The differences between single slit and double-slits diffraction is listed in table 7.1. The comparison of diffraction intensities of light for single slit and double slits is also shown in figure 7. 11. Table 7.1 Differences between single slit and double-slits diffraction Single-slit diffraction Consist of one slit Waves that originate within the same slit interfere Double-slits diffraction Consist of two slits Slits are so small that each one is considered as a single light source, and the interference of waves originating within the same slit can be neglected The fringes are broad and not as sharp The fringes are narrow and sharp as double-slit All bright fringes are visible Intensity: 0 = I-I \[sin (π a sin Some bright fringes are missing since they suppressed by the minima of a single-slit interference pattern Intensity: )/(л a sin2 1-1 cos2 \[ d sin \]\[sin (7 a sin)/( a sin)\]2 I=I light intensity **Single slit interference pattern** **Combined fringe pattern** **Double-slit interference pattern** *Figure 7.11 Comparison of diffraction intensities of light for single slit and double slits* Chapter 7 \| Interference, Diffraction and Polarization of Light (163)