Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
Mei Lin cannot see clearly any object that is farther than from her eyes. Her optician will fit a thin lens that sits right at her eye. Find the focal length and the power of the lens that lets her see distant objects clearly.
A thin lens at the eye must make the object look as if it were at the near point or the far point of the eye. Short sight: and . Long sight: . The power in dioptre is with in metre.
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Given. The far point is . The lens is at the eye.
Plan. The lens must form a virtual image of a very far object at the far point.
Step 1. The focal length. and . So and .
Step 2. The power. .
Answer: and . It is a concave lens.
Check. A short-sighted eye needs a diverging lens, so a negative power is right.
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