Answered: ** 25. What would be the radius of…

** 25. What would be the radius of curvature of a make-up mirror that produces a virt. mage of your face that is twice the size of your actual face, when you are standing 20 cm - ront of the mirror?

College Physics

1st Edition

ISBN:9781938168000

Author:Paul Peter Urone, Roger Hinrichs

Publisher:Paul Peter Urone, Roger Hinrichs

Chapter25: Geometric Optics

Section: Chapter Questions

Problem 57PE: What is the focal length of a makeup mirror that produces a magnification of 1.50 when a person’s...

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What is the focal length of a makeup mirror that produces a magnification of 1.50 when a person’s face is 12.0 cm away? Explicitly show how you follow the steps in the Problem-Solving Strategy: Spherical Mirrors.
Use the law of reflection to prove that the focal length of a mirror is hall its radius of curvature. That is, prove that f = R/2. Note this is true for a spherical mirror only if its diameter is small compared with its radius of curvature.
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 .
A dedicated sports car enthusiast polishes the inside outside surfaces of a hubcap that is a thin section of a sphere. When she looks into one side of the hubcap. she sees an image of her face 30.0 cm in back of the hubcap. She then flips the hubcap over and sees another image of her face 10.0 cm in back of the hubcap. (a) How far is her face from the hubcap? (b) What is the radius of curvature of the hubcap?
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.
What is the focal length of a makeup mirror that produces a magnification of 1.50 when a person’s face is 12.0 cm away? Explicitly show how you follow the steps in the ProblemSolving Strategy for Mirrors.
A nearsighted man cannot see objects clearly beyond 20 cm from his eyes. How close must he stand to a mirror in order to see what he is doing when he shaves?
Consider a spherical concave mirror with the object located to the left of the mirror beyond the focal point. Using ray diagrams, show that the image moves to the left as the object approaches the focal point.
A microscope has an objective lens with a focal length of 16.22 mm and an eyepiece with a focal length of 9.50 mm. With the length of the barrel set at 29.0 cm, the diameter of a red blood cells image subtends an angle of 1.43 mrad with the eye. It the final image distance is 29.0 cm from the eyepiece, what is the actual diameter of the red blood cell? Hint: To solve this question, go back to basics and use the thin-lens equation.
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 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.