Answer Physics Homework: Optics, Distance between Patient's Eyes & Glasses

[lolcheelol]

Homework Statement

A nearsighted patient's far point is 0.717 m from her eyes. She is able to see distant objects in focus when wearing glasses with a refractive power of -1.45 diopters. What is the distance between her eyes and the glasses?

di = 0.717m
refractive power = -1.45 diopters

Homework Equations

1/do + 1/di = 1/f
refractive = 1/f

The Attempt at a Solution

I first tried to put the refractive power into the focal point using the equation my book gave us.
-1.45 = 1/f
f = 1/-1.45

Then I set up the equation as best as I could

1/do + 1/.717 = 1/-1.45
-> 1/do = 1/-1.45 - 1/.717
-> 1/do = -2.084
-> do = -.4798

This answer wasn't correct and I don't even know if I'm doing it right...please help!

 

[anathema]

Hello, thank you for your question. It seems like you are on the right track with using the equations for calculating the distance of an object to a lens. However, there are a few things to consider in this problem that may be causing your answer to be incorrect.

First, the equation 1/do + 1/di = 1/f is used for calculating the focal length (f) of a lens, not the distance (do) of an object from the lens. In this problem, we are trying to find the distance between the patient's eyes and the glasses, not the focal length of the glasses.

Second, the refractive power (R) of a lens is equal to 1/f, not just f. So in this case, the refractive power of the glasses would be -1.45 diopters, which can be converted to -0.6897 meters^-1.

With these considerations, we can set up the following equation:

1/do + 1/di = R
-> 1/do = R - 1/di
-> do = 1/(R - 1/di)
-> do = 1/(-0.6897 - 1/-0.717)
-> do = 0.462 m

This means that the distance between the patient's eyes and the glasses is approximately 0.462 meters.

I hope this helps clarify the problem. Please let me know if you have any further questions.