The Wave Nature of Light Chapter 24

Properties of Light Properties of light include reflection, refraction, interference, diffraction, and dispersion. Ray diagrams model reflection and refraction (geometrical optics). Other properties can be understood by modeling light as a wave (wave optics). Note that properties of light can equivalently be modeled as a particle! This model involves quantum mechanics.

Properties of Light Geometrical optics describe how images can be formed using mirrors and lenses. Wave optics describe the colored patterns in a soap bubble, an oil slick, or on a CD.

Coherent Light Coherent light is light consisting of waves that are in phase with one another. Most light is not coherent (nor monochromatic)

Interference with Water Waves Notice bands of light and dark regions

Young’s Double Slit Experiment Interference with light is not easily observed because it has relatively short wavelengths and is not generally coherent or monochromatic. To produce two sources of coherent light, Young passed light first through a single slit to produce coherent light, then through two slits to produce two sources of coherent light.

Young’s Double Slit Experiment

Light waves incident on two slits form spherical waves. Where crests line up with crests, constructive interference occurs. Where crests line up with troughs, destructive interference occurs.

Young’s Double Slit Experiment

Math! For Constructive Interference, ΔL = nλ From the geometry, ΔL=dsinθ Substitute: for small angles θ, sinθ = tanθ = y/L So y = nLλ/d gives the location of the interference maxima for n = 0, 1, 2, 3…

Constructive vs Destructive Constructive: nλ = dsinθ nλ = d(y/L) y = nλL/d for n = 0, 1, 2 Destructiven(λ/2) = dsinθ n λ/2 = d(y/L) y = nλL/2d for n = 1, 3, 5, 7…

Example Monochromatic light passes through two narrow slits that are mm apart. The interference pattern is observed on a white wall 1.0 meter from the slits, and the second order maximum is at an angle of 1.5°. a) if the slit separation decreases, what happens to the angle? b) What is the wavelength of the light and what is the distance between the n=2 and n=3 interference fringes? c) if d = mm, what is θ 2 ?

Thin Film Interference Thin films of soap or oil produce colorful rainbow patterns! This optical effect is caused by reflection and interference. The colors that are seen must have wavelengths that interfere constructively…

Recall… When a wave reflects off of a medium or boundary that is more dense, it reflects inverted. When a wave reflects off of a medium or boundary that is less dense, it reflects right side up. Index of refraction gives a measure of ‘optical density’.

Thin Film Interference Incident light is reflected and refracted off of the first surface Refracted light is again reflected and refracted off of the second surface. What condition is necessary for constructive interference?

Thin Film Interference When the bottom layer is more dense than the middle layer, what condition is necessary for constructive interference?

Homework Read 24.1 and 24.2 Do # 7, 8, 11 – 13, 16, 25, 27 – 29, 33

Diffraction What would you see with Young’s Double Slit experiment if waves weren’t diffracted at the openings? i.e. If waves always traveled in straight lines like rays? Waves don’t always travel in straight lines… they spread out as they pass through the slits. They diffract.

Diffraction Diffraction is the spreading of a wave at an opening or around an edge or corner. Generally, the longer the wavelength compared with the width of the opening, the greater the diffraction.

Single Slit Diffraction The condition for relative minima is: wsinθ = mλ m = 1, 2, 3 Using sinθ = y/L y m = m(Lλ/w)

Single Slit Diffraction

Width of Central Maximum The width of the central maximum is twice the width from the center to the first minimum (2y 1 ) 2y 1 = 2Lλ/w

Example Monochromatic light passes through a slit whose width is 0.050mm. a) the general spreadout of the diffraction pattern is 1) larger for longer wavelengths 2) larger for shorter wavelengths b) At what angle will the third minimum be seen for λ = 400nm and λ = 550nm? c) What is the width of the central maximum on a screen located 1.0 m from the slit for those wavelengths?

Homework Read carefully about diffraction gratings on pages 772 – 774. Do # 36, 38, , 45, 48, 52, 53

Diffraction Gratings The interference pattern from a double slit is a pattern of bright bands (maxima). As the number of slits increase, the maxima (bright bands) become narrower and the minima (dark) wider Diffraction by a single slit causes a wide central maximum followed by bright and dark bands.

Diffraction Grating A diffraction grating consists of a large number of parallel, closely spaced slits. The resulting pattern is a combination of interference and diffraction… N = number of lines/cm d = 1/N gives distance between successive slits

Diffraction Grating The condition for maxima for a grating is given by dsinθ = nλ

Polarization Polarization describes the vibrational orientation of a light wave. Normally light is unpolarized. Light can become polarized by reflection, scattering, or by passing light through a polarizing filter.

Polarizing Filters Filters reduce intensity of light by allowing only one vibrational orientation to pass through the filter. When two filters are used, all light can be blocked.