Finding the optical power of a contact lens

In summary, a farsighted man uses eyeglasses with a refractive power of 2.05 diopters and a distance of 0.020 m from his eyes. He is able to read books held no closer than 0.265 m from his eyes. To find the correct prescription for contact lenses, the formula 1/do+1/di=1/f is used, where do is the object distance and di is the image distance. By plugging in the given values, the power of the contact lenses is calculated to be +1.38 diopters. This accounts for the increase in object distance of 0.020 m when using contact lenses instead of eyeglasses.
  • #1
ilovejava
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Homework Statement


A farsighted man uses eyeglasses with a refractive power of 2.05 diopters. Wearing the glasses 0.020 m from his eyes, he is able to read books held no closer than 0.265 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


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The image formed when wearing eyeglasses is 0.265-0.020 = 0.245 and this has to be negative because the man is using convex lenses, so d/i = -0.245 with eyeglasses. Next, I found the the object distance when wearing eyeglasses by using the formula 1/do+1/di=1/f and it turned out to be 0.163 the fact that it's positive makes sense because the object is placed in front of the lens. Now because the questions asks to find the power of the contact lenses the distance of the object when using contacts increases by 0.020m so do with lenses equals 0.183m. Finally I plugged everything into 1/do+1/di=1/f and got +1.38 diopters.
 
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  • #2
The 0.265 m distance is to the book, which is the object, not the image (for the glasses anyway)!
So what you are calculating for the glasses is the image distance produced by the glasses, which I get a different answer for, so please show your steps to that value so that we are on the same page.
 

Related to Finding the optical power of a contact lens

1. How is the optical power of a contact lens measured?

The optical power of a contact lens is measured in diopters (D) and is determined by the curvature of the lens. The flatter the curvature, the lower the diopter number, and the steeper the curvature, the higher the diopter number.

2. What is the process for finding the optical power of a contact lens?

The process for finding the optical power of a contact lens involves using a specialized instrument called a keratometer. This instrument measures the curvature of the cornea and provides a value in millimeters (mm). This value is then converted to diopters using a conversion formula.

3. Can the optical power of a contact lens change over time?

Yes, the optical power of a contact lens can change over time due to various factors such as age, eye health, and environmental factors. It is important to regularly visit an eye care professional to ensure the correct optical power is prescribed for your contact lenses.

4. Is the optical power of a contact lens the same for both eyes?

No, the optical power of a contact lens can vary between the left and right eye. This is because the cornea shape and curvature can differ slightly between the two eyes. It is important to have each eye individually measured for the correct optical power.

5. How does the optical power of a contact lens affect vision?

The optical power of a contact lens is crucial in correcting refractive errors such as nearsightedness, farsightedness, and astigmatism. It allows light to properly focus on the retina, providing clear vision. An incorrect optical power can lead to blurry or distorted vision.

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