Problem Solving Examples Department of Physics 72 Example 1 As shown in figure, a layer of water covers a slab of material X in a beaker. A ray of light traveling upward follows the path indicated. Using the information on the figure, find a) the index of refraction of material X b) the angle the light makes with the normal in the air. Department of Physics 74 Example 1 Department of Physics 74 Example 1 Department of Physics 74 Example 2 ▪ ▪ A ray of light incident on a surface of a 90° prism and emerges at the second surface such that the angle of refraction is 90°. Calculate the index of refraction of the prism if the incident angle is 𝜙1 is 40°. 𝜙1 𝜙2 𝜙3 𝜙4 Department of Physics 75 Example 2 Department of Physics 75 Example 2 Department of Physics 75 Example 2 Department of Physics 75 Example 2 Department of Physics 75 Example 2 Department of Physics 75 Example 2 Department of Physics 75 Example 3 ▪ Normal What should be the angle of incidence 𝜙 for glass (n=1.60) for the angle of refraction to be 𝜙/2? sin 𝜙 = 2 1 − cos 𝜙 2 𝜙 glass 𝜙 2 sin2 𝜙 + cos 2 𝜙 = 1 Department of Physics 76 Example 3 Department of Physics 76 Example 3 Department of Physics 76 Example 3 Department of Physics 76 SEATWORK A beaker with a mirrored bottom is filled with a liquid whose index of refraction is 1.63. A light beam strikes the top surface of the liquid at an angle of 42.5 from the normal. a) At what angle from the normal will the beam strikes the mirrored bottom of the beaker? b) At what angle from the normal will the beam exit from the liquid after traveling down through the liquid, reflecting from the mirrored bottom, and returning to the surface. Department of Physics 77 SEATWORK A beaker with a mirrored bottom is filled with a liquid whose index of refraction is 1.63. A light beam strikes the top surface of the liquid at an angle of 42.5 from the normal. a) At what angle from the normal will the beam strikes the mirrored bottom of the beaker? b) At what angle from the normal will the beam exit from the liquid after traveling down through the liquid, reflecting from the mirrored bottom, and returning to the surface. Department of Physics 77 SEATWORK Department of Physics 77 SEATWORK Department of Physics 77 SEATWORK Department of Physics 77 SEATWORK Department of Physics 77 Example 4 A parallel beam of unpolarized light in air is incident at an angle 54.5° (with respect to the normal) on a plane glass surface. The reflected beam is completely linearly polarized. (a) What is the refractive index of the glass? (b) What is the angle of refraction of the transmitted beam? Department of Physics 78 Example 4 A parallel beam of unpolarized light in air is incident at an angle 54.5° (with respect to the normal) on a plane glass surface. The reflected beam is completely linearly polarized. (a) What is the refractive index of the glass? (b) What is the angle of refraction of the transmitted beam? Department of Physics 78 Example 4 A parallel beam of unpolarized light in air is incident at an angle 54.5° (with respect to the normal) on a plane glass surface. The reflected beam is completely linearly polarized. (a) What is the refractive index of the glass? (b) What is the angle of refraction of the transmitted beam? Department of Physics 78 Example 5 A 1.00-cm-thick by 4.00-cm-long glass plate is made up of two prisms. The top prism has an index of refraction of 1.486 and the bottom prism has an n of 1.878. A light ray is incident on the top face as shown in the figure. The reflected ray A is completely linearly polarized. Determine the exit angle of this ray that pass through the prisms. 𝜃𝑝 𝜃𝑝 𝑛′ = 1.486 1.00 𝑐𝑚 𝑛′′ = 1.878 4.00 𝑐𝑚 Department of Physics 80 Example 5 Determine the exit angle of this ray that pass through the prisms. Department of Physics 80 Example 5 Determine the exit angle of this ray that pass through the prisms. Department of Physics 80 Example 5 Determine the exit angle of this ray that pass through the prisms. Department of Physics 80 Example 5 Determine the exit angle of this ray that pass through the prisms. Department of Physics 80 Example 5 Determine the exit angle of this ray that pass through the prisms. Department of Physics 80 Example 6 ● The light beam strikes surface 2 at the critical angle. Determine the angle of incidence 𝜃1 Department of Physics 81 Example 6 ● The light beam strikes surface 2 at the critical angle. Determine the angle of incidence 𝜃1 Department of Physics 81 Example 6 ● The light beam strikes surface 2 at the critical angle. Determine the angle of incidence 𝜃1 Department of Physics 81 Example 6 ● The light beam strikes surface 2 at the critical angle. Determine the angle of incidence 𝜃1 Department of Physics 81 Example 6 ● The light beam strikes surface 2 at the critical angle. Determine the angle of incidence 𝜃1 Department of Physics 81 Example 7 Three polarizing filters are stacked, with the polarizing axis of the second and third filters at angles of 60° and 90°, respectively, to that of the first. (a) What is the light intensity (in terms of ) at points and (b) If we remove the middle filter, what will be the light intensity at point C? Department of Physics 79 Example 7 Three polarizing filters are stacked, with the polarizing axis of the second and third filters at angles of 60° and 90°, respectively, to that of the first. (a) What is the light intensity (in terms of ) at points and (b) If we remove the middle filter, what will be the light intensity at point C? Department of Physics 79 Example 7 Three polarizing filters are stacked, with the polarizing axis of the second and third filters at angles of 60° and 90°, respectively, to that of the first. (a) What is the light intensity (in terms of ) at points and (b) If we remove the middle filter, what will be the light intensity at point C? Department of Physics 79 SEATWORK II Three polarizing filters are stacked, with the polarizing axis of the second and third filters at angles of 23.6 degrees and 62.2 degrees, respectively, to that of the first. If unpolarized light is incident on the stack, the light has an intensity of 75.5 W/cm2 after it passes through the stack. If the incident intensity is kept constant, what is the intensity of the light after it has passed through the stack if the second polarizer is removed? Department of Physics 79 SEATWORK II Department of Physics 79 SEATWORK II Department of Physics 79 SEATWORK II Department of Physics 79 End Page Click to edit title style Click to edit subtitle style