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Lecture #5 Diffraction: A Close Look PHYS102

Lecture #5 Diffraction: A Close Look PHYS102 . February, 1 st. The two workshops for this week: are titled: Squeezing Light for its Secrets: Diffraction Bring your calculator. Be prepared to go outdoors. .

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Lecture #5 Diffraction: A Close Look PHYS102

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  1. Lecture #5Diffraction: A Close Look PHYS102 February, 1st

  2. The two workshops for this week: are titled: Squeezing Light for its Secrets: Diffraction Bring your calculator. Be prepared to go outdoors.

  3. Review of what diffraction is:From an experimental point-of-view, there are two signposts of diffraction:When light goes through a small opening, it spreads out like a fan.There is no sharp shadow.  Instead, the image is blurred at its edges.The same statements hold, when light encounters an obstacle. Again, there is no sharp shadow.

  4. Diffraction is based on Huygens’s principle

  5. On close examination of the edges, we find: There are alternate regions of darkness and brightness. First known discovery of diffraction:  Observations by Francesco Grimaldi, a Jesuit priest, (1618 – 1663). He looked at sunlight entering a darkened room through a tiny hole in a screen. Found: The spot was enlarged, relative to expectations from a particle model of light. He examined the border of the image. Observed: Colored fringes. Grimaldi’s work was the first experimental evidence that light is a wave.

  6. Observation of diffraction Send single-colored (monochromatic) light through a single tiny slit. Observations: 1)The light has spread out, relative to when the slit is absent. 2)Alternate bright and dark regions (fringes).

  7. Pictures of diffraction fringes: 1) Observe light that passes through a pair of scissors:Note the circular patterns of bright and dark regions. Second picture: Light is sent through two openings: When the openings are large, no diffraction effects are apparent. But: When the openings are small, the image is fuzzy.  The spreading of light “blurs” the pictures.

  8. Quantitative ViewSingle Slit DiffractionSuppose we have parallel rays of light reaching a single slit of width a.Let λ be the wavelength of the light.We wish to explain why we see thealternate bright and dark fringes.Plot: Intensity versus location on screen:Note the maxima followed by minima.

  9. Now, calculate the location of the first dark fringe, relative to the center of the screen. Consider two rays. One starts from the slit-center: Ray #1 The other starts from the bottom of the slit: Ray #2. The distance, along the slit-length, between starting-points, is a/2. Select the point P so that the two rays have a path-difference to P exactly equal to λ/2. They interfere destructively at P.

  10. Let θ be the angle that the line from P to the center of the slit makes with the initial ray direction. Then, from the definition of the sine of an angle, the path difference is (a/2) sin θ = λ/2. Multiplying by 2 we get the useful result: a sin θ = λ. This gives the result for the angle θ for the first minima.

  11. What about all the other rays to P from the slit? They also produce destructive interference in pairs. Why? Consider a ray slightly above the bottom ray. That ray will be cancelled, at P, by a ray that is the same distance above the slit-center. By the same argument, any ray in the lower half of the slit is cancelled by a ray in the upper half. This justifies the result

  12.  a sin θ = λ.  We can compute the wavelength λ of light from this relation, plus diffraction experiment measurement of θ. As in the case of the Young experiment, the result for λ depends on the color.  The result for λ:  Roughly 400 nm for violet light  Roughly 700 nm for red light.  The Young experiment gives similar results.  Important point:  Both experiments reveal that differing colors differ in their wavelength.

  13. This Week’s Workshop You will see light diffracted through a circular opening. The result for the location of the first minima turns out to be slightly different from the result for a slit.  It is: θ = 1.22 λ/D. Here, D is the diameter of the opening. You will use this relation to measure the wavelength λ of light in this week’s workshops. Important note: The angle θ is measured in radians.  

  14. Quizz questions (Feb 1st, 2005): 1. Is the light a wave or a particle? 2. What is a simple harmonic motion? 3. What is the wavelength? 4. What is the interference? 5. What is the wave-relation between speed, and wavelength?

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