1. 1. A farsighted man uses eyeglasses with a refractive power of 4.01 diopters.

Question

1. 1. A farsighted man uses eyeglasses with a refractive power of 4.01 diopters. Wearing the glasses 0.015 m from his eyes, he is able to read books held no closer than 0.290 m from his eyes. He would like a prescription for contact lenses to serve the same purpose. What is the correct contact lens prescription, in diopters?

2. To focus a camera on objects at different distances, the converging lens is moved toward or away from the image sensor, so a sharp image always falls on the sensor. A camera with a telephoto lens (f = 179.1 mm) is to be focused on an object located first at a distance of 3.5 m and then at 50.0 m. Over what distance must the lens be movable? The answer isn't 0.11

Explanation / Answer

focal length f = 1/P = 1/4.01 = 0.25 m

object distance for lens s = 0.29 - 0.015 = 0.275 m

image distance s' = ?

1/s + 1/s' = 1/f

1/0.275 + 1/s' = 1/0.25

image distance s' = 2.75 m

near point D = 2.75 - 0.015 = 2.735 m

1/0.29 + 1/2.735 = 1/f

f = 0.262 m

correct contactlens = 1/f = 3.82 Diopters

==========================

2)

for object distance s1 = 3.5 m

1/s1 + 1/s1' = 1/f

1/3.5 + 1/s1' = 1/0.1791

s1' = 0.189 m

for

for object distance s2 = 50 m

1/s2 + 1/s2' = 1/f

1/50 + 1/s2' = 1/0.1791

s2' = 0.18 m

s1' - s2' = 0.189-0.18 = 0.09 m <<<<----ANSWER

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