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**Thin Films, Diffraction, and Double slit interference**

IB – Option A

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**Young's Experiment Construction is reinforcement (adding).**

Suppose you have two waves with the same phase at point P, and L1 and L2 are the length the waves have traveled. The waves differ by one wavelength: So L1 = 2¼ l and L2 = 3¼ l Whenever L2 - L1 = ml, where m = 1,2,3,…, there is constructive interference.

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**Cont. Destruction is cancellation (subtraction)**

Suppose you have two waves that are out of phase at point P, and L1 and L2 are the length the waves have traveled The waves differ by one-half a wavelength So L1 = 2¾ l and L2 = 3¼ l So whenever L2-L1 = (m + ½)l, where m = 0,1,2,3…, there is destructive interference

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Coherent Sources Two sources are coherent if the waves they emit maintain a constant phase relation. This means the wave do not shift relative to one another Lasers are coherent, incandescent bulbs are non coherent

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Young In 1801, Thomas Young demonstrated the wave nature of light by overlapping light waves and showing interference He was also able to determine the wavelength of light When the path difference is = l, a bright fringe is made When the path difference an odd multiple of ½ l, a dark fringe is made

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**Two Slit Interference For Bright Fringes, For Dark Fringes,**

M = fringe order 0,1,2,3…. l = wavelength d = slit separation Θ Angle from normal to “fringe.”

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**Diffraction The bending of waves around obstacles**

Christian Huygens ( ) describes that Every point on a wave front acts as a source of tine wavelet that move forward with the same speed as the wave. The wave front at a later instant is the surface that is tangent to the wavelets. The amount of bending is determined by l/ W, where W is the width of the opening For dark fringes sinq = ml/W

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Diffraction Grating Consists of a flat barrier which contains many parallel slits separated by a short distance d. A parallel monochromatic light beam passing through the grating is diffracted by an angle θ similar to two slit interference. However, the intensity of the diffracted light is higher and the peaks are much narrower.

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Resolution Because light bends, it’s sometime hard to distinguish one light source from another.

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Rayleigh Criterion For resolution of two object by a circular lens of diameter D the diffraction limit of resolution occurs when the image of the second object is at position of the first minimum of the diffraction pattern of the first object. B = diameter of circular opening

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Sample Question The camera of a spy satellite orbiting at 200 km has a diameter of 35 cm. What is the smallest distance this camera can resolve on the surface of the earth? (Assume a wavelength of 500 nm) First calculate q. Now calculate s from s = r q.

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**Polarization Electromagnetic radiation i.e. Light**

Plane, monochromatic wave Electric and magnetic fields are Orthogonal In phase Transverse to direction of propagation

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Polarization When light is polarized, the electric field always points in the same direction. polarized in the vertical direction: The electric field points in the vertical direction. unpolarized: Superposition of many beams, approximately parallel, but each with random polarization. Every atom in the filament of an incandescent bulb radiates a separate wave with random phase and random polarization.

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**Polarization Can also be caused by reflection.**

When reflected off a non-metallic surface, light becomes partially polarized. The angle of incidence that cause complete polarization in called Brewster's Angle:

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Polarization uses Stress analysis LCD’s

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X-rays

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**Thin-Film Interference**

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Chapter 24 Wave Optics. Young’s Double Slit Experiment Thomas Young first demonstrated interference in light waves from two sources in 1801. Light is.

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