At age 45, a person is fitted for reading glasses that have a power equal to 2.2

Question

At age 45, a person is fitted for reading glasses that have a power equal to 2.23 D in order to read at 25.0 cm. By the time she reaches the age of 55, she discovers herself holding her newspaper at a distance of 42.0 cm in order to see it clearly with her glasses on. Assume the glasses are placed 2.2 cm from her eyes.

(a) Where was her near point at age 45?
   cm

(b) Where is her near point at age 55?
m

(c) What power is now required for the lenses of her reading glasses so that she can again read at 25.0 cm?
D

Explanation / Answer

Part 1)

The focal length is the inverse of the dioptic power

1/2.23 = .448 (which is 44.8 cm)

Then apply 1/f = 1/p + 1/q (p is the distance from the paper to the lens)

p = 25-2.2 = 22.8 cm

1/44.8 = 1/22.8 + 1/q

q = -46.4 cm

Thus the near point is 46.4 + 2.2 = 48.6 cm from her eyes

Part B)

Same idea, new onject distance...

p = 42 - 2.2 = 39.8 cm

1/44.8 = 1/39.8 + 1/q

q = -353.9 cm

Thus the near point is 353.9 + 2.2 = 356.1 cm from her eyes

Part C)

1/f = 1/p + 1/q

1/f = 1/22.8 + 1/-353.9

f = 24.4 cm

D = 1/f (in meters)

D = 1/.244

D = 4.10

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