Focal length of her contact lenses

In summary, Anne's homework statement is to find the focal length of her contact lenses so that she can see clearly objects as close as 24.0 cm from her eye. The Attempt at a Solution suggests that she should use the same focal length as the viewer's biological lens when working at his/her limit of vision. Both approaches should work out to the same result.
  • #1
phy112
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Homework Statement



Anne is farsighted; the nearest object she can see clearly without corrective lenses is 2.4 m away. It is 1.8 cm from the lens of her eye to the retina.

What should the focal length of her contact lenses be so that she can see clearly objects as close as 24.0 cm from her eye?

Homework Equations



1/p+1/q=1/f. I keep getting 1.67 and this is wrong and i am stuck

The Attempt at a Solution

 
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  • #2
What units do they want the answer in?
 
  • #3
You'll need to find a few things:
First, find the focal length of the biological lens in the viewer's eye when he/she is working at his/her limit of vision.
Then find the required focal length the viewer should have to view the closer object.

Then consider: how do these two differ?
The contact lens is placed right up next to the lens in the viewers eye, so you can consider the net focal length required to be the sum of the contact lens and the viewer's lens in his/her eye. It's much easier than the case of case of eyeglasses... which have a separation between the two lenses (the eyeglass lens and the eye lens itself).

There's another way to approach the problem also.
First, where would the viewers eye place the image of the object that is too close?
Second, make THAT image the object for a second lens (at the position of the eye)... and you know where you WANT to place the second image of this... right at the back of the eye.
Drawing out scaled ray-tracing for this technique might help.
This second approach is, in fact, the only way to approach the eyeglasses problem, in which case you should then know where the glasses will sit in relation to the person's eye.

Both ways should work out to the same result. DO as Kurdt says, watch your units (and be consistent in them!). It's also easy to goof up all the math, since you are working with reciprocals of the distances and focal lengths.
 

1. What is the focal length of contact lenses?

The focal length of contact lenses refers to the distance between the lens and the eye where the light rays converge to form a clear image on the retina. It is typically measured in millimeters (mm) and can vary depending on the type of contact lens.

2. How does the focal length affect vision with contact lenses?

The focal length of contact lenses determines the strength of the lens, which affects how light is refracted to correct vision. A shorter focal length means a stronger lens, which is used to correct nearsightedness, while a longer focal length is used to correct farsightedness.

3. Can the focal length of contact lenses be adjusted?

No, the focal length of contact lenses cannot be adjusted. It is determined by the curvature and thickness of the lens, which are designed specifically for each individual's prescription. However, different types of contact lenses with varying focal lengths are available to correct different types of vision problems.

4. How does the focal length of contact lenses compare to glasses?

The focal length of contact lenses is usually shorter than that of glasses because they sit directly on the eye, while glasses sit a distance away from the eye. This allows contact lenses to correct vision with less distortion and a wider field of view.

5. Can wearing contact lenses with the wrong focal length cause vision problems?

Yes, wearing contact lenses with the wrong focal length can cause vision problems such as blurry vision, eye strain, and headaches. It is important to get a proper eye exam and prescription from an optometrist to ensure the correct focal length is used for your contact lenses.

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