Physics 123

24. Light: Geometric Optics 24.1 Waves versus Particles 24.2 Huygens’ Principle 24.3 Young’s double-slit Interference 24.5 Single-slit Diffractin 24.6 Diffraction Grating 24.7 Spectrometer and Spectroscopy 24.8 Thin-film Interference

Is Light a Wave or a Particle? Particles travel in a straight line Particles cast a sharp shadow Diffraction Waves can bend into the shadow region Sound waves can bend around the corner Water waves can bend around a log Do light waves bend?

Waves exhibit Interference and Diffraction Do light waves bend around obstacles (Diffraction)? Do light waves exhibit Interference?

Huygens’ Principle Every point on a wavefront can be considered as a source of wavelets that spread out at the speed of the wave itself

Young’s double-slit Interference

Problem Young’s Experiment Young’s double-slit experiment provided incontrovertible evidence in support of the wave nature of light. In a modern version of the experiment, red light from a He-Ne laser with a wavelength of 700 nm is used. The distance between the slits is 1 mm and the screen is 2m away. The separation between the bright fringes will be most nearly A. 2 mm B. 6 mm C. 1 cm D. 10 cm

Solution Young’s Experiment Bright Fringes occur when the path difference equals a whole number of wavelengths. d sin  = 0 (central maximum) d sin  = (First maximum) But sin  = x / L d x / L = x = L / d x = 2.1 mm

Single-slit Diffraction

If w sin  = then the waves from the top half of the slit will have a path difference of /2 relative to the waves from the bottom half. The net result will be a dark fringe For dark fringe : w sin  = m (m =1,2,3 ….) If m = 0, there is a wide, central bright maximum

Single-slit Diffraction Pattern

Problem Single-slit Diffraction Yellow light with = 600 nm falls on a slit of width 0.3 mm. The screen is 2m from the slit. The width of the central maximum is A. 2 mm B. 4 mm C. 6 mm D. 8 mm

Solution Single-slit Diffraction Position of the first dark fringe is given by x = L / w (see problem 24.1 !!!) x = 4 mm So the width of the central maximum is 8 mm

Diffraction Grating Instead of just 2 slits as in Young’s double- slit experiment, we use 10,000 slits per cm or more!!! This yields sharper maxima and minima and larger separation between the bright and dark fringes.

Spectrometer

Problem Spectrometer The replica grating has 10,000 lines/cm. A first order violet line is observed at 25 degrees. The wavelength of the line is most nearly A. 425 nm B. 450 nm C. 475 nm D. 500 nm

Solution Spectrometer Maxima occur when d sin  = m First order means m = sin 25 0 = = 423 nm

Thin-film Interference Why do soap bubbles have such pretty colors?