Concept explainers
A person looking into an empty container is able to see the far edge of the container’s bottom, as shown in Figure P22.23a. The height of the container is h, and its width is d. When the container is completely filled with a fluid of index of refraction n and viewed from the same angle, the person can see the center of a coin at the middle of the container’s bottom, as shown in Figure P22.23b. (a) Show that the ratio h/d is given by
(b) Assuming the container has a width of 8.00 cm and is filled with water, use the expression above to find the height of the container.
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Chapter 22 Solutions
COLLEGE PHYSICS V1+WEBASSIGN MULTI-TERM
- Figure P36.95 shows a thin converging lens for which the radii of curvature of its surfaces have magnitudes of 9.00 cm and 11.0 cm. The lens is in front of a concave spherical mirror with the radius of curvature R = 8.00 cm. Assume the focal points F1 and F2 of the lens are 5.00 cm from the center of the lens, (a) Determine the index of refraction of the lens material. The lens and mirror are 20.0 cm apart, and an object is placed 8.00 cm to the left of the lens. Determine (b) the position of the filial image and (c) its magnification as seen by the eye in the figure. (d) Is the final image inverted or upright? Explain.arrow_forwardA floating strawberry illusion is achieved with two parabolic mirrors, each having a focal length 7.50 cm, facing each other as shown in Figure P33.58. If a strawberry is placed on the lower mirror, an image of the strawberry is formed at the small opening at the center of the top mirror, 7.50 cm above the lowest point of the bottom mirror. The position of the eye in Figure P35.58a corresponds to the view of the apparatus in Figure P35.58b. Consider the light path marked A. Notice that this light path is blocked by the upper mirror so that the strawberry itself is not directly observable. The light path marked B corresponds to the eye viewing the image of the strawberry that is formed at the opening at the top of the apparatus. (a) Show that the final image is formed at that location and describe its characteristics. (b) A very startling effect is to shine a flashlight beam on this image. Even al a glancing angle, the incoming light beam is seemingly reflected from the image! Explain. Figure P35.58arrow_forwardIn Figure P35.30, a thin converging lens of focal length 14.0 cm forms an image of the square abed, which is he = hb = 10.0 cm high and lies between distances of pd = 20.0 cm and pa = 30.0 cm from the lens. Let a, b, c. and d represent the respective corners of the image. Let qa represent the image distance for points a and b, qd represent the image distance for points c and d, hb, represent the distance from point b to the axis, and hc represent the height of c. (a) Find qa, qd, hb, and hc. (b) Make a sketch of the image. (c) The area of the object is 100 cm2. By carrying out the following steps, you will evaluate the area of the image. Let q represent the image distance of any point between a and d, for which the object distance is p. Let h represent the distance from the axis to the point at the edge of the image between b and c at image distance q. Demonstrate that h=10.0q(114.01q) where h and q are in centimeters. (d) Explain why the geometric area of the image is given by qaqdhdq (e) Carry out the integration to find the area of the image. Figure P35.30arrow_forward
- How many times will the incident beam in Figure P34.33 (page 922) be reflected by each of the parallel mirrors? Figure P34.33arrow_forwardWhy is the following situation impossible? Consider the lensmirror combination shown in Figure P35.55. The lens has a focal length of fL = 0.200 m, and the mirror has a focal length of fM = 0.500 m. The lens and mirror are placed a distance d = 1.30 m apart, and an object is placed at p = 0.300 m from the lens. By moving a screen to various positions to the left of the lens, a student finds two different positions of the screen that produce a sharp image of the object. One of these positions corresponds to light leaving the object and traveling to the left through the lens. The other position corresponds to light traveling to the right from the object, reflecting from the mirror and then passing through the lens. Figure P35.55 Problem 55 and 57.arrow_forwardThe left face of a biconvex lens has a radius of curvature of magnitude 12.0 cm, and the right face has a radius of curvature of magnitude 18.0 cm. The index of refraction of the glass is 1.44. (a) Calculate the focal length of the lens for light incident from the left. (b) What If? After the lens is turned around to interchange the radii of curvature of the two faces, calculate the focal length of the lens for light incident from the left.arrow_forward
- Two converging lenses having focal lengths of f1 = 10.0 cm and f2 = 20.0 cm are placed a distance d = 50.0 cm apart as shown in Figure P35.48. The image due to light passing through both lenses is to be located between the lenses at the position x = 31.0 cm indicated. (a) At what value of p should the object be positioned to the left of the first lens? (b) What is the magnification of the final image? (c) Is the final image upright or inverted? (d) Is the final image real or virtual?arrow_forwardConsider 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_forwardAn object is placed a distance of 10.0 cm to the left of a thin converging lens of focal length f = 8.00 cm, and a concave spherical mirror with radius of curvature +18.0 cm is placed a distance of 45.0 cm to the right of the lens (Fig. P38.129). a. What is the location of the final image formed by the lensmirror combination as seen by an observer positioned to the left of the object? b. What is the magnification of the final image as seen by an observer positioned to the left of the object? c. Is the final image formed by the lensmirror combination upright or inverted? FIGURE P38.129arrow_forward
- Consider a light ray traveling between air and a diamond cut in the shape shown in Figure P22.42. (a) Find the critical angle for total internal reflection for light in the diamond incident on the interface between the diamond and the outside air. (b) Consider the light ray incident normally on the top surface of the diamond as shown in Figure P22.42. Show that the light traveling toward point P in the diamond is totally reflected. (c) If the diamond is immersed in water, find the critical angle at the diamond−water interface. (d) When the diamond is immersed in water, does the light ray entering the top surface in Figure P22.42 undergo total internal reflection at P ? Explain. (e) If the light ray entering the diamond remains vertical as shown in Figure P22.42, which way should the diamond in the water be rotated about an axis perpendicular to the page through 0 so that light will exit the diamond at P ? (f) At what angle of rotation in part (e) will light first exit the diamond at…arrow_forwardThe light beam in Figure P22.43 strikes surface 2 at the criticalangle. Determine the angle of incidence, Θ1.arrow_forwardUsing filters, a photographer has created a beam of light consisting of three wavelengths: 400 nm (violet), 500 nm (green), and 650 nm (red). She aims the beam so that it passes through air and then enters a block of crown glass. The beam enters the glass at an incidence angle of θ1 = 41.6°. The glass block has the following indices of refraction for the respective wavelengths in the light beam. wavelength (nm) 400 500 650 index of refraction n400 nm = 1.53 n500 nm = 1.52 n650 nm = 1.51 (a) Upon entering the glass, are all three wavelengths refracted equally, or is one bent more than the others? 400 nm light is bent the most 500 nm light is bent the most 650 nm light is bent the most all colors are refracted alike (b) What are the respective angles of refraction (in degrees) for the three wavelengths? (Enter each value to at least two decimal places.) (i) θ400 nm ° (ii) θ500 nm ° (iii) θ650 nm °arrow_forward
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