Question

(1.) Nearsightedness (a.) A nearsighted person has a far point that is 323 cm from her eye. Her lens in a pair of glasses is 2 cm in front of her eye. What focal length is required to cast the image of a far-away object at her far point? (b.) If these glasses are used to view an object 525 cm from her eye, where do her glasses cast the image? In both cases, quote your distance as measured from the eye, not the glasses. (2.) Farsightedness (a.) A farsighted person wears glasses that enable him to read a book held at a distance of 25 cm frorm his eyes, even though his near-point is 57 cm. If his glasses are 2 cm from his eyes, find the focal length and refractive power (1/f) required of his lenses to place the image of the book at the near point. A second person has a near-point distancet the lenses required for this person greater than or less than the refractive power in part (a.)? To check, calculate the refractive strength for a near-point distance of 67.0 cm.

Answer 1

1) The far point is 323 cm from eye means we want the image to be appearing at 323 cm from eye. Here object distance is infinity

so,

1/f = 1/di + 1/do

1/f = 1/323 + 0

f = - 323 cm or -3.23 m ( a concave lens is required)

If the object is 525 cm,

then 1/di = 1/f - 1/do

1/di = -1/323 - 1/525

di = - 199.97 cm

so distance of image will be 199.97 cm from eye

2 ) f = 57 *25 / 57 -25

f = 44.5 cm from the eye ( a converging lens is required)

P = 1/f = 1/0.445 = 2.245 Diopters. (To calulate power, convert f from cm to m)