Optics Wave Behavior in Optics Diffraction

Transcription

1 Optics Wave Behavior in Optics Diffraction Lana Sheridan De Anza College June 15, 2018

2 Last time Interference of light: the Double-Slit experiment multiple slit interference diffraction gratings

3 Overview X-ray diffraction diffraction patterns

4 X-ray Diffraction X-rays can be used to study the structure of matter. The wavelength of X-rays is around 0.1 nm. ( nm) This is roughly the interatomic spacing. Layers of atoms can act as a diffraction grating!

5 X-ray Diffraction represent Na ions. a Incident beam The incident beam can reflect from different planes of atoms. Reflected beam Upper plane Lower plane u d sin u u u d Figure A two-dimensional description of the The ray reflecting from the lower layer travels an extra path length of 2d sin θ. Bragg s Law 2d sin θ = mλ m Z +

6 Diffraction Patterns and Polarization X-ray Diffraction Photographic film Crystal X-ray beam X-ray source when the film was exposed. This image is what one sees when looking through the holographic film. Holograms are finding a number of applications. You may have a hologram on your credit card. This special type of hologram is called a rainbow hologram and is designed to be viewed in reflected white light Diffraction of X-Rays by Crystals NaCl x-ray crystallograph from another crystal In principle, the wavelength of any electromagnetic wave can be determined if a

7 such as telescopes, cameras, and eyeglasses. Diffraction 35.4 Analysis Model: Wave Under Reflection We already know that light and other waves that travel through a small We introduced gap (< λ) the diverge, concept of and reflection that the of waves smaller in a the discussion gap, the of waves moreon strings in Section As with waves on strings, when a light ray traveling in one divergence. medium encounters a boundary with another medium, part of the incident light When l,, d, the rays continue in a straight-line path and the ray approximation remains valid. When l d, the rays spread out after passing through the opening. When l.. d, the opening behaves as a point source emitting spherical waves. d l,, d l d l.. d a b c The intensity of light in each direction is not the same however. Figure wavelen rier in of diam

8 Diffraction Patterns alternating with dark fringes. Incoming wave Slit min max min u max min max L min Viewing screen a b

9 Diffraction Spikes 1 NASA, ESA, and H. Richer (University of British Columbia); Svon Halenbach

10 Diffraction Spikes in Camera Apertures Iris diaphragms adjust the amount of light allowed into a camera body. They cause characteristic diffraction patterns on photos taken of bright lights. 1 Wikipedia user Cmglee

11 Diffraction Patterns: Arago Spot Directly in the center of the shadow produced by a round object lit with coherent light, a spot of light can be observed! This is called the Arago spot, Fresnel bright spot, or Poisson spot. 1 Photo taken at Exploratorium in SF, own work.

12 by much weaker maxima Understanding the Diffraction alternating Pattern with dark fromfringes. a Single Slit Incoming wave Slit min max min u max min max L min Viewing screen

13 Diffraction and Huygens Principle The new wave front is drawn tangent to When we have a slit or aperture the illuminated circular wavelets by coherent radiating light, from eachthe part of the aperture acts as a point sources of on spherical the original wavelets. front. A B c t Old wave front c t New wave front Old wave front N f A B a b These wavelets interfere to produce a diffraction pattern.

14 Understanding the Diffraction Pattern from a right Single of th Slit Each portion of the slit acts as difference a point source of light waves. Consider a series of point sources in different parts of the slit. between The r slit has width a. difference the pairs o 5 lation occu 4 because th the upper a a/2 a/2 u a sin u or, if we c below,

15 Understanding the Diffraction Pattern from a Single Slit We can find minima (dark fringes) in the pattern by breaking up our point sources into pairs that cancel each other out. Matching point sources in the top half of the slit with ones in the bottom half, the source separation distances will be d = a/2. This will be a fringe dark when: δ = a 2 sin θ = λ 2

16 Understanding the Diffraction Pattern from a Single Slit However, we could also break the slit up into 4 equal parts and match sources from the 1st and 2nd, and match from the 3rd and 4th. This will be dark when: δ = a 4 sin θ = λ 2 If we break the slit up into 6 equal parts and match sources from the 1st and 2nd, the 3rd and 4th, and the 5th and 6th. This will be dark when: δ = a 6 sin θ = λ 2

17 Understanding the Diffraction Pattern from a Single Slit In general we expect dark fringes when: sin θ min = m λ a where m = ±1, ±2, ±3,...

18 Summary X-ray diffraction diffraction patterns Collected Homework! due Monday, June 18. Final Exam 9:15-11:15am, Tuesday, June 26. Homework Serway & Jewett: prev: Ch 38, onward from page CQs: 5; Probs: 25, 60 new: Ch 38, OQs: 3, 5; Probs: 1, 7, 10, 41