Optics: Eyeglasses.
9. A retired bank president can easily read the fine print of the financial page when the newspaper is held no closer than arm’s length, 60.0 cm from the eye. What should be the focal length of an eyeglass lens that will allow her to read at the more comfortable distance of 24.0 cm?
10. A person has far points 84.4 cm from the right eye and 122 cm from the left eye. Write a prescription for the powers of the corrective lenses.
11. The accommodation limits for Nearsighted Nick’s eyes are 18.0 cm and 80.0 cm. When he wears his glasses, he is able to see faraway objects clearly. At what minimum distance is he able to see objects clearly?
12. The near point of an eye is 100 cm. A corrective lens is to be used to allow this eye to clearly focus on objects 25.0 in front of it. (a) What should be the focal length of the lens? (b) What is the power of the needed corrective lens?
13. An individual is nearsighted; his near point is 13.0 cm and his far point is 50.0 cm. (a) What lens power is needed to correct his nearsightedness? (b) When the lenses are in use, what is this person’s near point?
16. PhysicsNow A person is to be fitted with bifocals. She can see clearly when the object is between 30 cm and 1.5 m from the eye. (a) The upper portions of the bifocals (Fig. P25.16) should be designed to enable her to see distant objects clearly. What power should they have? (b) The lower portions of the bifocals should enable her to see objects comfortably at 25 cm. What power should they have?
Figure P25.16
Solutions:
25.9 This patient needs a lens that will form an upright, virtual image at her near point (60.0 cm) when the object distance is . From the thin lens equation, the needed focal length is
25.10 For the right eye, the lens should form a virtual image of the most distant object at a position 84.4cm in front of the eye (that is, when ). Thus, , and the power is
Similarly, for the left eye and
25.11 His lens must form an upright, virtual image of a very distant object () at his far point, 80.0cm in front of the eye. Therefore, the focal length is .
If this lens is to form a virtual image at his near point (), the object distance must be
25.12 (a) The lens should form an upright, virtual image at the near point when the object distance is . Therefore,
(b) The power is
25.13 (a) The lens should form an upright, virtual image at the far point for very distant objects . Therefore, , and the required power is
(b) If this lens is to form an upright, virtual image at the near point of the unaided eye , the object distance should be
25.16 (a) The upper portion of the lens should form an upright, virtual image of very distant objects at the far point of the eye . The thin lens equation then gives , so the needed power is
(b) The lower part of the lens should form an upright, virtual image at the near point of the eye when the object distance is . From the thin lens equation,
Therefore, the power is