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WaveOptics

# WaveOptics - Wave Optics-1 Wave Nature of Light Light is a...

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Wave Optics-1 Wave Nature of Light Light is a wave, an electromagnetic wave. The wavelength λ of visible light is very small. Visible light: λ = 400 nm (violet) 700 nm (red) c = λ f , f = c / λ , λ = c / f Wave-like effects are difficult to detect because of the small wavelength. In many situations, light behaves like a ray, exhibiting no obvious wave-like behavior. Newton (late 1600's) did not believe that light was a wave since he always observed ray- behavior. Wave-like behavior was not clearly observed until around 1800. Review of Constructive/Destructive interference of Waves: Consider 2 waves, with the same speed v, the same wavelength λ , (and therefore same frequency f = c / λ ), traveling in the same (or nearly the same) direction, overlapping in the same region of space: If the waves are in phase , they add constructive interference Last update: 2/27/2012 Dubson Phys2020 Notes, University of Colorado big hole D >> λ : ray-behavior Light passing through hole in wall: tiny hole D λ : wave-behavior wavefronts λ = +

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Wave Optics-2 If the waves are out of phase , they subtract destructive interference If wave in nearly the same direction: Huygen's Principle: Each point on a wavefront (of given f, λ ) can be considered to be the source of a spherical wave. To see interference of light waves, you need a monochromatic (single λ ) light source, which is coherent (nice, clean plane wave). This is not easy to make. Most light sources are incoherent (jumble of waves with random phase relations) and polychromatic (many different wavelengths). Young's Double slit experiment (1801) : Last update: 2/27/2012 Dubson Phys2020 Notes, University of Colorado = + add subtract plane wave λ spherical wave (same λ , f ) speed c c c wall with infinitesimal hole
Wave Optics-3 What do you expect to see on the screen? If you believe light is a ray, then you expect to see 2 bright patches on the screen, one patch of light from each slit. But here is what you actually see: A series of bright and dark fringes: wave interference How do we explain this? Consider the 2 slits as 2 coherent point sources of monochromatic light. Two sources are coherent is they have the same wavelength λ (and therefore the same frequency f ) and they emit peaks and troughs in sync , in phase. Each slit (source) emits light in all forward directions, but let us consider only the parts of the waves heading toward a particular point on the screen. Last update: 2/27/2012 Dubson Phys2020 Notes, University of Colorado monochromatic plane wave λ d 2 slits screen c position x on screen Intensity I d x I

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Wave Optics-4 If the screen is far away (L >> d), then the rays from the two slits to the same point on the screen are nearly parallel, both heading in the same direction, at the same angle
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