Chapter 36 Diffraction

Goals for Chapter 36 To define and explain Fresnel and Fraunhofer diffraction To consider single-slit diffraction To summarize and then apply an understanding of diffraction gratings To consider the atomic example of x-ray diffraction To study circular apertures and resolving power To introduce holography

Introduction It’s intuitive that sound can diffract (and travel around corners). Light doesn’t “show its poker hand” so easily. If you shine light from a point source to a ruler and look at the shadow, you’ll see the edges are … well … not sharp. A close inspection of the indistinct edge will reveal fringes. This phenomenon may not sound useful yet but stay with us until the end of Chapter 36. This line of thinking has shown the way for advances in DVD technology and applications in holography.

Fresnel and Fraunhofer diffraction According to geometric optics, a light source shining on an object in front of a screen will cast a sharp shadow. Surprisingly, this does not occur.

Diffraction and Huygen’s Principle Diffraction patterns can be analyzed as we did in Section 33.7 using Huygen’s Principle. Recall, every source of a wave front can be considered to be the source of secondary waves. Superposition of these waves results in diffraction. If the source and the screen are close to the edge causing the diffraction, the effect is called “near-field” or Fresnel diffraction. If these objects are far apart, so as to allow parallel-ray modeling, the diffraction is called “far-field diffraction” or Fraunhofer diffraction.

Diffraction from a single slit The result is not what you might expect. Refer to Figure 36.3.

Dark fringes in single-slit diffraction Consider Figure 36.4 below. The figure illustrates Fresnel and Fraunhofer outcomes.

Fresnel or Fraunhofer? The previous slide outlined two possible outcomes but didn’t set conditions to make a choice. Figure 36.5 (below) outlines a procedure for differentiation.

Fraunhofer diffraction and an example of analysis Figure 36.6 (at bottom left) is a photograph of a Fraunhofer pattern from a single slit. Follow Example 36.1, illustrated by Figure 36.7 (at bottom right).

Intensity in a single-slit pattern Following the method we used in Section 35.5, we can derive an expression for the intensity distribution.

Intensity maxima in a single-slit pattern The expression for peak maxima is iterated for the strongest peak. Consider Figure 36.9 that shows the intensity as a function of angle.

Interference from multiple slits The approximation of sin θ = θ is very good considering the size of the slit and the wavelength of the light. Consider Figure 36.10 at the bottom of the slide. Follow Example 36.2. Follow Example 36.3.

Multiple slit interference The analysis of intensity to find the maximum is done in similar fashion as it was for a single slit. Consider Figure 36.12 at right. Consider Figure 36.13 below.

Several slits Consider Figure 36.14 at right. Consider 36.15 below.

A range of parallel slits, the diffraction grating Two slits change the intensity profile of interference; many slits arranged in parallel fashion are now termed as rulings. Consider Figures 36.16 and 36.17 at right. Consider Figure 36.18 below. Follow Example 36.4.

The grating spectrograph A grating can be used like a prism, to disperse the wavelengths of a light source. If the source is white light, this process is unremarkable, but if the source is built of discrete wavelengths, our adventure is now called spectroscopy. Chemical systems and astronomical entities have discrete absorption or emission spectra that contain clues to their identity and reactivity. See Figure 36.19 for a spectral example from a distant star.

The grating spectrograph II—instrumental detail Spectroscopy (the study of light with a device such as the spectrograph shown below) pervades the physical sciences.

X-ray diffraction X-rays have a wavelength commensurate with atomic structure. Rontgen had only discovered this high-energy EM wave a few decades earlier when Friederich, Knipping, and von Laue used it to elucidate crystal structures between adjacent ions in salt crystals. The experiment is shown below in Figure 36.21.

Ionic configurations from x-ray scattering Arrangements of cations and anions in salt crystals (like Na+ and Cl– in Figure 36.22 … not shown) can be discerned from the scattering pattern they produced when irradiated by x-rays.

X-ray scattering set Watson and Crick to work An x-ray scattering pattern recorded by their colleague Dr. Franklin led Watson and Crick to brainstorm the staircase arrangement that eventually led to the Nobel Prize. Follow Example 36.5, illustrated by Figure 36.25 below.

Circular apertures and resolving power In order to have an undistorted Airy disk (for whatever purpose), wavelength of the radiation cannot approach the diameter of the aperture through which it passes. Figures 36.26 and 36.27 illustrate this point.

Using multiple modes to observe the same event Multiple views of the same event can “nail down” the truth in the observation. Follow Example 36.6, illustrated by Figure 36.29.

Holography—experimental By using a beam splitter, coherent laser radiation can illuminate an object from different perspective. Interference effects provide the depth that makes a three-dimensional image from two-dimensional views. Figure 36.30 illustrates this process.

Holography—theoretical The wavefront interference creating the hologram is diagrammed in Figure 36.31 below.

Holography—an example Figure 36.32 shows a holographic image of a pile of coins. You can view a hologram from nearly any perspective you choose and the “reality” of the image is astonishing.