last dance Chapter 26 – diffraction – part ii Presentation slide for courses, classes, lectures et al. last dance Chapter 26 – diffraction – part ii Instructor Course

What’s Going On?? Today – Finish (?) Diffraction Tuesday – Nothing – No room is available for a review session. Wednesday – Examination #4 – Material that we covered in chapters 24, 25 and 26. Friday – Complete semester’s material. Start Review Next Monday – Wrap-up and overview of the course. December 12 - SATURDAY – 9:00AM – Psychology Building Room PSY 108. BE THERE!!! Last Mastering Physics Assignment Posted. No more! Ever!

Last Time – Two Slit Interference

From another world .. sound. Two small loudspeakers that are 5.50 m apart are emitting sound in phase. From both of them, you hear a singer singing C# (frequency 277 Hz), while the speed of sound in the room is 340 m/s. Assuming that you are rather far from these speakers, if you start out at point P equidistant from both of them and walk around the room in front of them, at what angles (measured relative to the line from P to the midpoint between the speakers) will you hear the sound (a) maximally enhanced? Neglect any reflections from the walls.

Table m sin(q)=ml/d q degrees 1 0.223636364 0.225544 13.26728 2 1 0.223636364 0.225544 13.26728 2 0.447272727 0.463714 27.27728 3 0.670909091 0.735434 43.26083 4 0.894545455 1.107413 65.14195 5 1.118181818 ? - 6 1.341818182

Diffraction Huygens’ principle requires that the waves spread out after they pass through narrow slits This spreading out of light from its initial line of travel is called diffraction In general, diffraction occurs when waves pass through small openings, around obstacles or by sharp edges

Diffraction Grating The diffracting grating consists of many equally spaced parallel slits of width d A typical grating contains several thousand lines per centimeter The intensity of the pattern on the screen is the result of the combined effects of interference and diffraction

Diffraction Grating The condition for maxima is d sin θbright = m λ The integer m is the order number of the diffraction pattern If the incident radiation contains several wavelengths, each wavelength deviates through a specific angle

Diffraction Grating, 3 All the wavelengths are focused at m = 0 This is called the zeroth order maximum The first order maximum corresponds to m = 1 Note the sharpness of the principle maxima and the broad range of the dark area This is in contrast to the broad, bright fringes characteristic of the two-slit interference pattern Active Figure: The Diffraction Grating

DIFFRACTION GRATING PATTERN

CD=Diffraction Grating

A shadow isn’t simply a shadow.

But what about this???

This effect is called DIFFRACTION What about shadows??? Bright Center Fringes Shadow of a small steel ball Reality This effect is called DIFFRACTION

Diffraction Vs. Interference Both involve addition of waves from different places and technically, both are the same phenomenon. Observation requires monochromatic light and a small, coherent light source. If you are close to a source (non paraxial approx) we call it Fresnel Diffraction or near-field diffraction. Far away we call it Fraunhofer or far-field diffraction Diffraction usually refers to a continuous source of wavelets adding up. Interference has a finite number of sources for which the phase is constant over each “source”.

Another case - Geometrical Shadow

Adding waves a piece at a time.. Maxima q D WHY?? Single Slit Screen

WHY?

Single-Slit Diffraction A single slit placed between a distant light source and a screen produces a diffraction pattern It will have a broad, intense central band – central maximum The central band will be flanked by a series of narrower, less intense secondary bands – secondary maxima The central band will also be flanked by a series of dark bands – minima The results of the single slit cannot be explained by geometric optics Geometric optics would say that light rays traveling in straight lines should cast a sharp image of the slit on the screen

Single-Slit Diffraction Fraunhofer Diffraction occurs when the rays leave the diffracting object in parallel directions Screen very far from the slit Converging lens (shown) A bright fringe is seen along the axis (θ = 0) with alternating bright and dark fringes on each side

Single-Slit Diffraction According to Huygens’ principle, each portion of the slit acts as a source of waves The light from one portion of the slit can interfere with light from another portion All the waves that originate at the slit are in phase Wave 1 travels farther than wave 3 by an amount equal to the path difference δ = (a/2) sin θ Similarly, wave 3 travels farther than wave 5 by an amount equal to the path difference δ = (a/2) sin θ

Single-Slit Diffraction If the path difference δ is exactly a half wavelength, the two waves cancel each other and destructive interference results δ = ½ λ = (a/2) sin θ  sin θ = λ / a In general, destructive interference occurs for a single slit of width a when sin θdark = mλ / a m = 1, 2, 3, …

Single-Slit Diffraction A broad central bright fringe is flanked by much weaker bright fringes alternating with dark fringes The points of constructive interference lie approximately halfway between the dark fringes ym = L tan θdark , where sin θdark = mλ / a

25. •A beam of laser light of wavelength 632 25. •A beam of laser light of wavelength 632.8 nm falls on a thin slit 0.00375 mm wide. After the light passes through the slit, at what angles relative to the original direction of the beam is it completely cancelled when viewed far from the slit?

27. •Parallel light rays with a wavelength of 600 nm fall on a single slit. On a screen 3.00 m away, the distance between the first dark fringes on either side of the central maximum is 4.50 mm. What is the width of the slit?

30. •Light of wavelength 633 nm from a distant source is incident on a slit 0.750 mm wide, and the resulting diffraction pattern is observed on a screen 3.50 m away. What is the distance between the two dark fringes on either side of the central bright fringe?

35. •A laser beam of wavelength 600 35. •A laser beam of wavelength 600.0 nm is incident normally on a transmission grating having 400.0 lines/mm. Find the angles of deviation in the first, second, and third orders of bright spots.

38. •(a) What is the wavelength of light that is deviated in the first order through an angle of 18.0° by a transmission grating having 6000 lines/cm? (b) What is the second-order deviation for this wavelength? Assume normal incidence.

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