15. * Sinking ships A legend says that Archimedes once saved his native town of Syracuse byburning the enemy's fleet with mirrors. Describe quantitatively the type of mirrors thatArchimedes could have used to burn ships that were 150 m away. Justify your answer.

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Answered: 15. * Sinking ships A legend says that…

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter26: Image Formation By Mirrors And Lenses

Section: Chapter Questions

Problem 3P

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A periscope (Fig. P23.5) is useful for viewing objects that cannot be seen directly. It can be used in submarines and when watching golf matches or parades from behind a crowd of people. Suppose the object is a distance p from the upper mirror and the renters of the two fat mirrors air separated by a distance h. (a) What is the distance of the final image from the lower mirror? (b) Is the final image real or virtual? (c) Is it upright or inverted? (d) What is its magnification? (e) Does it appear to be left-right reversed? Figure P23.5
Why is your vision so blurry when you open your eyes while swimming under water? How does a face mask enable clear vision?
A periscope (Fig. P23.5) is useful for viewing objects that cannot be seen directly. It can be used in submarines and when watching golf matches or parades from behind a crowd of people. Suppose the object is a distance p from the upper mirror and the renters of the two fat mirrors air separated by a distance h. (a) What is the distance of the final image from the lower mirror? (b) Is the final image real or virtual? (c) Is it upright or inverted? (d) What is its magnification? (e) Does it appear to be left-right reversed? Figure P23.5
To fit a contact lens to a patient's eye, a keratometer can be used to measure the curvature of the corneathe front surface of the eye. This instrument places an illuminated object of known .size at a known distance p from the cornea, which then reflects some light from the object, forming an image of it The magnification M of the image is measured by using a small viewing telescope that allows a comparison of the image formed by the cornea with a second calibrated image projected into the field of view by a prism arrangement. Determine the radius of curvature of the cornea when p = 30.0 cm and M = 0.013 0.
To fit a contact lens to a patient's eye, a keratometer can be used to measure the curvature of the corneathe front surface of the eye. This instrument places an illuminated object of known .size at a known distance p from the cornea, which then reflects some light from the object, forming an image of it The magnification M of the image is measured by using a small viewing telescope that allows a comparison of the image formed by the cornea with a second calibrated image projected into the field of view by a prism arrangement. Determine the radius of curvature of the cornea when p = 30.0 cm and M = 0.013 0.
A diverging lens has a focal length of 20.0 cm. Use graph paper to construct accurate ray diagrams for object distance of (a) 40.0cm and (b) 10.0 cm. In each case, determine the location of the image from the diagram and the image magnification, and state whether the image is uptight or inverted. (c) Estimate the magnitude of uncertainty in locating the points in the graph. Are your answers and the uncertainty consistent with the algebraic answers found in Problem 33?
Andy decides to use an old pair of eyeglasses to make some optical instruments. He knows that the near point in his left eye is 50.0 cm and the near point in his right eve is 100 cm. (a) What is the maximum angular magnification he can produce in a telescope? (b) If he places the lenses 10.0 cm apart, what is the maximum overall magnification he can produce in a microscope? Hint: Go back to basics and use the thin lens equation to solve part (b).
A converging lens in a vertical plane receives light from an object and forms an inverted image on a screen. An opaque card is then placed next to the lens, covering only the upper half of the lens. What happens to the image on the screen? (a) The upper half of the image disappears. (b) The lower half of the image disappears. (c) 'The entire image disappears, (d) The entire image is still visible, but is dimmer. (e) No change in the image occurs.
A dance hall is built without pillars and with a horizontal ceiling 7.20 m above the floor. A mirror is fastened flat against one section of the ceiling. Following an earthquake, the mirror is in place and unbroken. An engineer makes a quick check of whether the ceiling is sagging by directing a vertical beam of laser light up at the mirror and observing its reflection on the floor. (a) Show that if the mirror has rotated to make an angle with the horizontal, the normal to the mirror makes an angle with the vertical. (b) Show that the reflected laser light makes an angle 2 with the vertical. (c) Assume the reflected laser light makes a spot on the floor 1.40 cm away from the point vertically below the laser. Find the angle .
Using the law of reflection, explain how powder takes the shine off of a person’s nose. What is the name of the optical effect?
A Fermats principle of least time for refraction. A ray of light traveling in a medium with speed v1 leaves point A and strikes the boundary between the incident and transmitted media a horizontal distance x from point A as shown in Figure P38.98. The refracted ray travels with speed v2 in the second medium, eventually reaching point B. The horizontal distance between points A and B is L. a. Calculate the time t required for the light to travel from A to B in terms of the parameters labeled in the figure. b. Now take the derivative of t with respect to x. What is the condition for which the ray of light will take the shortest time to travel from A to B? Figure P38.98
A simple model of the human eye ignores its lens entirely. Most of what the eye does to light happens at the outer surface of the transparent cornea. Assume that this surface has a radius of curvature of 6.00 mm and that the eyeball contains just one fluid with a refractive index of 1.40. Prove that a very distant object will be imaged on the retina, 21.0 mm behind the cornea. Describe the image.

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15. * Sinking ships A legend says that Archimedes once saved his native town of Syracuse by burning the enemy's fleet with mirrors. Describe quantitatively the type of mirrors that Archimedes could have used to burn ships that were 150 m away. Justify your answer.