Change the chapter
Question
A myopic person sees that her contact lens prescription is –4.00 D . What is her far point?
Question by OpenStax is licensed under CC BY 4.0.
$25.0\textrm{ cm}$
Solution Video

OpenStax College Physics for AP® Courses Solution, Chapter 26, Problem 18 (Problems & Exercises) (2:15)

Sign up to view this solution video!

Rating

No votes have been submitted yet.

Quiz Mode

Why is this button here? Quiz Mode is a chance to try solving the problem first on your own before viewing the solution. One of the following will probably happen:

  1. You get the answer. Congratulations! It feels good! There might still be more to learn, and you might enjoy comparing your problem solving approach to the best practices demonstrated in the solution video.
  2. You don't get the answer. This is OK! In fact it's awesome, despite the difficult feelings you might have about it. When you don't get the answer, your mind is ready for learning. Think about how much you really want the solution! Your mind will gobble it up when it sees it. Attempting the problem is like trying to assemble the pieces of a puzzle. If you don't get the answer, the gaps in the puzzle are questions that are ready and searching to be filled. This is an active process, where your mind is turned on - learning will happen!
If you wish to show the answer immediately without having to click "Reveal Answer", you may . Quiz Mode is disabled by default, but you can check the Enable Quiz Mode checkbox when editing your profile to re-enable it any time you want. College Physics Answers cares a lot about academic integrity. Quiz Mode is encouragement to use the solutions in a way that is most beneficial for your learning.

Calculator Screenshots

OpenStax College Physics, Chapter 26, Problem 18 (PE) calculator screenshot 1
Video Transcript
This is College Physics Answers with Shaun Dychko. This person has a contact lens prescription with a power of negative 4.00 diopters and the question is what is their far point without any contact lenses on? So their far point with the contact lenses will be infinity because that's the goal of the lenses is to create normal vision, which has a far point of infinity. So this change in power is the difference between the power for normal vision— looking at the far point— minus the power with no correction when looking at their far point and so this is 1 over the normal object distance of the far point which is infinity plus 1 over the image distance, which is the distance between the lens and the retina and then we'll subtract from that the power for uncorrected vision for this person, which is 1 over their far point which is what we have to find here plus 1 over the same image distance as before because this is a distance inside the eye between the lens and the retina. So this 1 over d i works out to zero here because it's plus 1 over d i minus positive 1 over d i and so this makes zero there and we are left with 1 over normal object distance in the far point minus 1 over object distance without correction. So the normal far point is infinity so this fraction is zero then and so we have a negative 1 over d o is ΔP. So negative 1 over their far point without correction is this correction provided by the contact lens. So we can raise both sides to exponent negative 1 and we have d o then is negative 1 over ΔP— I guess I multiplied both sides by negative 1 here too by the way to move the negative sign to the other side— so that's negative of 1 over negative 4.00 diopters which is positive 0.250 meters, which is 25.0 centimeters. So their far point is what a regular vision can see at its closest so this is as far away as they can see, it is 25.0 centimeters.