Concept explainers
You are working for a solar energy company. Your supervisor has asked you to investigate a new idea that has been proposed for a solar collector. A large sphere of glass focuses light on photocells, as shown in Figure P35.22. The photocells are moved by electronics along the curved track to the right of the sphere. Your supervisor would like to build a prototype of a material with index of refraction n, but needs for you to calculate the position at which the Sun’s rays focus and, therefore, to find where to locale the curved track.
Figure P35.22
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Chapter 35 Solutions
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- Consider a light ray that enters a pane of glass with air on one side and water on the other side as shown in Figure P38.21. The light ray experiences refraction at the first interface when it enters the glass from the water and again at the second interface when it exits the glass into the air. Assume the index of refraction of the glass is 1.54. For a ray of light, find the angle of incidence 1 in the water such that the ray experiences total internal reflection when it strikes the glassair interface on the other side. FIGURE P38.21arrow_forwardAs shown in Figure P35.73, a light ray is incident normal to one face of a 30°-60°-90° block of flint glass (a prism) that is immersed in water. (a) Determine the exit angle θ3 of the ray.(b) A substance is dissolved in the water to increase the index of refraction n2. At what value of n2 does total internal reflection cease at point P?arrow_forwardQ1/ Consider a laser cavity consisting of a concave mirror and a convex mirror, separated by 2m as shown in the figure. . Given R1=R2 = 2m, where R1 and R2 are the radii of curvatures of the concave and convex mirrors, respectively. Obtain the matrix representing the ray transformation for one complete round trip in the cavity?arrow_forward
- A green laser beam travels through the an L-shaped block of transparent blue plastic with an angle 00 = 38. above the x axis. The index of refraction of the blue plastic is nb = 1.90. The beam passes into a rectangular block of transparent yellow plastic, and the refracted ray then has an angle of Oy = 43., as shown in the figure below. %3D a. What is the speed of the laser beam as it travels through the blue plastic? b. What is the index of refraction ny of the yellow plastic? c. When the refracted laser beam reaches the other edge of the yellow plastic, it is refracted again as it re-enters the blue plastic. What is the final direction Of of the beam above the x axis?arrow_forwardWhen the light illustrated in Figure P35.21 passes through the glass block, it is shifted laterally by the distance d. Find the time interval required for the light to pass through the glass block, where t = 1.50 cm, n = 1.50, and = 35.0⁰ ps Figure P35.21arrow_forwardStudents in a lab group are given a plastic cube with a hollow cube-shaped space in the middle that fills about half the volume of the cube. The index of refraction of the plastic is known. The hollow space is filled with a gas, and the students are asked to collect the data needed to find the index of refraction of the gas. What information would you need to collect, and how would you use this information in order to deduce the index of refraction of the gas in the cube?arrow_forward
- 34. Consider a beam of light from the left entering a prism of apex angle O as shown in Figure P34.34. Two angles of incidence, 0, and 0,, are shown as well as two angles of refraction, 0, and 0,. Show that O = 0, + 0g- 2 %D 2 3°arrow_forwardA drop of water (n=1.33) in the shape of a hemisphere with radius 3.0 mm sits on smooth horizontal surface of a sapphire (n=1.77). A thin laser beam enters the droplet from air and reaches the water-sapphire boundary at the exact center of their circle of contact. At that point, laser beam is completely reflected off the surface of the sapphire. a. What is the maximum height above the sapphire that the laser beam could enter the droplet to be internally reflected at the center of the droplet as described above? b. What is the angle of incidence as the beam enters the droplet?arrow_forwardLight is incident on a prism as shown in Figure P38.31. The prism, an equilateral triangle, is made of plastic with an index of refraction of 1.46 for red light and 1.49 for blue light. Assume the apex angle of the prism is 60.00. a. Sketch the approximate paths of the rays for red and blue light as they travel through and then exit the prism. b. Determine the measure of dispersion, the angle between the red and blue rays that exit the prism. Figure P38.31arrow_forward
- A Lucite slab (n = 1.485) 5.00 cm in thickness forms the bottom of an ornamental fish pond that is 40.0 cm deep. If the pond is completely filled with water, what is the apparent thickness of the Lucite plate when viewed from directly above the pond?arrow_forwardN A fish is 3.25 m below the surface of still water. Because of total internal reflection, it is hidden from the view of a fisher in a boat on the water as long as the boat is outside a circle of radius r. The center of the circle is directly above the fish (Fig. P38.16). Find the minimum value of r.arrow_forwardYou are working for an electronics company that makes devices for the home. Your supervisor has given you an assignment to help design the projection mechanism for a projection alarm clock. In this type of clock, a projection system is mounted on the body of the clock, as shown in Figure P35.31a, where the projection system is the silver cylinder, of radius R = 3.25 cm, mounted on the left side of the clock. A converging lens is mounted on the edge of the cylinder. Inside the cylinder, a small digital display of the time in red characters can be moved from the center of the cylinder outward radially toward the lens. The red light of the digital display can he seen in the lens in Figure P35.31a. As a result, an image of the time is projected in red onto the ceiling or wall of a darkened room (Fig. P35.31b). The range of distances for focused images of the digital display is from 0.500 m to 4.00 m, measured from the center of the cylinder. For the smallest value of the range, the digital display is at the center of the cylinder. You must determine for your supervisor the following parameters for the design of the projection system: (a) the focal length of the lens and (b) the distance of the digital display from the center of the cylinder for the largest value of the range. Figure P35.31arrow_forward
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