B. Wave optics 1. Huygens’ principle Huygens’ principle: Every point on a wave front acts as a point source; the wavefront as it develops is tangent to their envelope. 1) Waves Versus Particles Huygens’ Principle and Diffraction (qualitative descreption) 2) Huygens’ Principle and the Law of Refraction As the wavelets propagate from each point, they propagate more slowly in the medium of higher index of refraction. This leads to a bend in the wavefront and therefore in the ray. The frequency of the light does not change, but the wavelength does as it travels into a new medium. Mirage Question: What is changed, when a light wave enters into a medium of different optical density? A) its speed and frequency B) its speed and wavelength C) its frequency and wavelength D) its speed, frequency & wavelength 2. Interference Interference – combination of waves (an interaction of two or more waves arriving at the same place) Important: principle of superposition Valley Peak (b) (a) Valley Waves source (b) (a) No shift or shift by r2 r1 m Shift by r2 r1 m 12 m 0,1,2,... (a) If the interfering waves add up so that they reinforce each other, the total wave is larger; this is called “constructive interference”. (b) If the interfering waves add up so that they cancel each other, the total wave is smaller (or even zero); this is called “destructive interference”. 3. Young’s experiment (Double-Slit Interference) d sin Depending on the path length difference between the slits and the screen, the wave can interfere constructively (bright spot) or destructively (dark spot). d sin m m - constructi ve d sin m m 12 - destructiv e m 0,1,2,.. R m y m R tan m R sin m m - constructi ve d m 12 ym R - destructiv e d ym R Example: In a double-slit experiment, it is observed that the distance between adjacent maxima on a remote screen is 1.0 cm. What happens to the distance between adjacent maxima when the slit separation is cut in half? A) It increases to 2.0 cm. B) It increases to 4.0 cm. C) It decreases to 0.50 cm. D) It decreases to 0.25 cm. Example: Monochromatic light falls on two very narrow slits 0.048 mm apart. Successive fringes on a screen 5.00 m away are 6.5 cm apart near the center of the pattern. What is the wavelength of the light? d 0.048mm R 5.00m y1 6.5cm ? m ym R - constructi ve d y1 d R 2 6 . 5 10 m 0.048 10 3 m 624.10 9 m 624nm 5.00m 4. Dispersion 1) Dispersion in Young’s experiment Since the position of the maxima (except the central one) depends on wavelength, the first- and higher-order fringes contain a spectrum of colors. 2) Dispersion of visible light Example: yr yv m 1 y r 3.5mm R d y v 2.0mm 2.0mm v 700nm 400nm 3.5mm r 700nm v ? y r v yv v r yr Example: The separation between adjacent maxima in a double-slit interference pattern using monochromatic light is A) greatest for red light. B) greatest for green light. C) greatest for blue light. D) the same for all colors of light. 3) The visible spectrum and dispersion The index of refraction of a material varies somewhat with the wavelength of the light. This variation in refractive index is why a prism will split visible light into a rainbow of colors. Rainbows Actual rainbows are created by dispersion in tiny drops of water.