Physics 012 1st Edition Lecture 27 Outline of Last Lecture I. If λ of light is large compared to size of opening that light passes through, we must consider diffraction and interference effects.a. Diffractioni. When light passes through a thin slit it will spread out with curved wave fronts.b. Constructive Interferencei. When light waves of equal amplitude and wavelength are completely in-phase, the amplitude of the resulting wave will have an amplitude twice that the individual light waves.c. Destructive Interferencei. When light waves of equal amplitude and wavelength are completely out-of-phase, the resulting light wave will have an amplitude of zero (completely dark).d. Laser Double-Slit Experimenti. Experiment: Coherent monochromatic light of wavelength λ is incident upon a screen with two narrow slits. λ is much greater than the width of the slits. A screen is placed a distance L from the screen with slits. These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.ii. Where wave fronts meet, there is constructive interference. Where a wave front of one light beam is directly between two wave fronts of the other light beam, there is destructive interference.iii. When projected onto a screen, a series of bright and dark spaces are observed. The bright space at the center is considered mc = 0, counting outwards with subsequent bright spots (mc = 1, mc = 2, etc). The dark spaces to either side of mc = 0 are considered md = 0, counting outwards with subsequent dark spots (md = 1, md = 2, etc).1. Intensity decreases as m increases.iv. The difference in the distance travelled by the light beam coming from one slit to point P and the distance travelled by the light beam coming from the other slit to point P is called the path length difference and is denoted δ.1. If δ is some multiple of λ (λ, 2λ, 3λ, etc.), there is constructive interference at point P.2. If δ is some half multiple of λ (λ/2, 3λ/2, 5λ/2, etc.), there is destructive interference at point P.Outline of Current Lecture II. Double-slit experimenta. When L is much larger than d, you can assume the two light beams (from each slit) are essentially parallel.i. d = distance between slits, L = distance between screens, m = fringe order(central = 0, first = 1, etc.), λ = light wavelength, θ = angle the normal line to the first screen and the light beams, y = vertical displacement of the light beamsii. dsinθ = mλ (for constructive interference)iii. tanθ = y/Liv. y = (mλL)/db.III. Diffraction Gratingsa. Like double-slit experiment but with many slits.b. d = distance between 2 successive slitsc. If experiment were in a medium other than air: y = [(mL)/d][λvac/n]IV. Change in Phase Due to Reflectiona. When a light beam is going from a medium with a lower index of refraction to a medium with a higher index of refraction (n1 < n2), the reflected light will undergoa phase change.i. The reflected light will be out of phase by exactly half a wavelength (λ/2).ii. No phase change occurs when n1 > n2.b.V. Thin Film
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