When a ray of light strikes a nonmetallic surface, some of the light is reflected and some  is refracted. Brewster’s angle is the angle of incidence for which the reflected and  refracted beams are 90 degrees apart. The significance of this angle is that it leads to a reflected ray which is completely polarized. (a) Sketch the incident, reflected, and refracted rays for a situation involving Brewster’s  angle. (b) Compute Brewster’s angle for water. The the index of refraction of water is 1.33 and the trigonometric identity sin(90degrees −θ) = cosθ

Three sheets of plastic have unknown indices of refraction. Sheet 1 is placed on top of sheet 2, and a laser beam is directed onto the sheets from above so that it strikes the interface at an angle of 26.6deg with the normal. The refracted beam in sheet 2 makes an angle of 31.4deg with the normal. The experiment is repeated with sheet 3 on top of sheet 2 and, with the same angle of incidence, the refracted beam makes an angle of 36.8deg with the normal. If the experiment is repeated again with sheet 1 on top of sheet 3, what is the expected angle of refraction in sheet 3? Assume the same angle of incidence.

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…

A laser beam with a total power of 22 watts is incident at a normal angle of incidence on a Lambertian surface. How much power reaches a detector with an area of 0.1 cm2 at an angle of 25 degrees located at a distance of 40 cm from where the beam strikes the surface? Please check closest answer.   0.525 mW   0.397 mW   0.247 mW   0.421 mW