Physics · Unit 6: Optics ·  Problem 6-2-1

Vision Aid Design

Three clients can’t see something they need. Pick one, work out the exact lens that helps, and show with numbers that it meets their need within their budget  ·  1 class day

Starring1/f = 1/d_o + 1/d_iP = 1/f (diopters)
Nearsighted: a close far point
Distant things are blurry. A diverging lens (negative power) makes a distant object’s virtual image appear at the far point, so P = −1 ÷ far point.
Farsighted: a distant near point
Close things are blurry. A converging lens (positive power) puts a book’s virtual image out at the near point, so P = 1 ÷ d_o − 1 ÷ near point.

🧭 Plot Summary

An optometrist’s waiting room has three people in it. One is a man who can’t read the label on his pill bottle. One is a student who can’t read the board. One is a man who has to hold a book at arm’s length to read it. Each of them needs a lens, and each lens has to be the right lens, in a size and at a price the client can actually use.

You’ll pick one client and design for them. The key idea is that a corrective lens doesn’t repair an eye. It places a virtual image of the thing the client is looking at where their eye can focus, at the near point or the far point. You’ll use the lens equation to find that lens, check it against every number in the client’s file, and then explain it to them in plain language, including what it can’t do.

What you will do in this problem

  • Meet three clients who can’t see something they need: a man who can’t read his pill bottle, a student who can’t read the board, and a man who can’t read a book.
  • Pick one client and work out exactly what lens would help them, using the lens equation and their eye measurements.
  • Check your lens against every constraint in the client’s file, such as price, size, and how it behaves in a second situation.
  • Explain to the client, in plain language, why your design works and what it can’t do.

Why it matters

This is the unit’s payoff. Mirrors, refraction, and lenses were the parts. Here you put them to work for a real person with a real limit on size or cost, which is exactly what an optical engineer does, and it’s the last problem of the course.

✅ Self-Check Before You Roll On

Check off each item as you get there. These are not grades — they are your own signal.