A farsighted man with eyeglasses problem

[KendrickLamar]

Homework Statement

A farsighted man uses eyeglasses with a refractive power of 2.20 diopters. Wearing the glasses 0.03 m from his eyes, he is able to read books held no closer than 0.28 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?

Homework Equations

1/do + 1/di = 1/f

The Attempt at a Solution

well starting off i figured if the power is +2.20 dipoeters then the fd is going to be -1/2.20
not sure but since with the glasses it would be 1/fd-.03? and then with the contacts what would happen since there no distance? I am just really confused now lol

 

[KendrickLamar]

500 views no replies? any ideas?? anyone lol!?

 

[ehild]

Find out at what distance d from the eye the image forms with the ordinary eyeglasses when the book is held at 0.28 m from the eye. What should be the focal distance when the lens is on the eye and the distance of the image is equal to d in the same situation?

ehild

 

[wutiantai]

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[Nickie]

Based on the given information, we can use the thin lens equation to find the correct prescription for contact lenses. The thin lens equation is 1/do + 1/di = 1/f, where do is the object distance, di is the image distance, and f is the focal length of the lens. In this case, the object distance is 0.28 m and the image distance is 0.03 m (since the man can read books held no closer than 0.28 m from his eyes with his glasses on). We can rearrange the equation to solve for f, which represents the focal length of the contact lenses:

1/f = 1/do + 1/di
1/f = 1/0.28 + 1/0.03
1/f = 3.57 + 33.33
1/f = 36.90
f = 1/36.90
f = 0.027 m

Now, we can use the formula for refractive power, P = 1/f, to find the correct prescription for the contact lenses. The refractive power is measured in diopters, so we can convert the focal length from meters to diopters by dividing it by 0.01 (since 1 diopter is equal to 1/m):

P = 1/f
P = 1/0.027
P = 37 diopters

Therefore, the correct prescription for the contact lenses is +37 diopters. This will provide the same refractive power as the glasses with a power of +2.20 diopters when the contact lenses are placed at a distance of 0.03 m from the eyes.