a light wave along ray r1 reflects once from a mirror and a light wave along ray r2 reflects twice from that same mirror and once from a tiny mirror at distance L from the bigger mirror. (Neglect the slight tilt of the rays.) The waves have wavelength 620 nm and are initially in phase. (a)What is the smallest value of L that puts the final light waves exactly out of phase? (b)With the tiny mirror initially at that value of L, how far must it be moved away from the bigger mirror to again put the final waves out of phase?

Sound waves with frequency 2600 Hz and speed 343 m/s diffract through the rectangular opening of a speaker cabinet and into a large auditorium of length 100 m. The opening, which has a horizontal width of 38.7 cm, faces a wall 100 m away (the figure below).   Along that wall, how far from the central axis of that wall in meters will a listener be at the first diffraction minimum and thus have difficulty hearing the sound? (Neglect reflections.)

Refractive Index (n) is a ratio of the speed of light in a vacuum to the speed of light in materials such as glass, water, plastic, etc. Using Snell's Law, and given an air to glass interface with and angle of incidence of 15 degrees, what will be the angle of refractance R if the refractive index of the glass is 1.5 ? Snell's Law: n; (sin I) = n, (sin R) So, Sin R = n; (sin I) / n And, R = arcsin (n; (sin I) / n,) For each angle I, find angle R: 5. I=0, R = 6. I=45, R = 7. I= 60, R = 8. I = 75, R = = arcsin (1(.259)/1.5) = arcsin (.172) = 9.9 degrees Wavelength in Air- Light- Angle of Light -Wavelength in Glass Normal 90° R Air nj-1 Glass

Two light sources of identical strength are placed 10m apart. An object is to be placed at a point P on a line l, parallel to the line joining the light sources and at a distance d meters from it (see the figure). We want to locate P on, so that the intensity of illumination is minimized. We need to use the fact that the intensity of illumination for a single source is directly proportional to the strength of the source and inversely proportional to the square of the distance from the source. a) Find an expression for the intensity l(x) at the point P. b) If d = 5m, use graphs of l(x) and l'(x) to show that the intensity is minimized when x = 5m, that is, when P is at the midpoint of l. c) If d = 10m, show that the intensity (perhaps surprisingly) is not minimized at the midpoint. d) Somewhere between d = 5m and d = 10m there is a transitional value of d at which the point of minimal illumination abruptly changes. Estimate this value of d by graphical methods. Then find the exact value…