Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
Alejandra is short-sighted and also cannot focus on very near things. At an eye test, her optician measures her range of clear vision. Without glasses she sees clearly only objects between and from her eye, as in the figure. The optician gives her a concave lens of focal length . She wears it right at her eye, and the lens is thin, so its distance from the eye can be ignored.
Find the power of the lens. Find the nearest object that she can see clearly with the lens on. Then decide whether the lens lets her see objects at infinity clearly. Her friend Tomas says that the lens gives her a nearer near point, because the lens helps the eye to focus. Show with the lens formula what happens to her near point, and say whether Tomas is right. Remember that her eye can still use only an image that lies inside her old range of clear vision, whatever the lens does to the rays.
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 old near point is , the old far point is , and for the lens at the eye.
Plan. The lens makes a virtual image of the object. Her eye can see the image if it is between and from the eye.
Step 1. The power. .
Step 2. The farthest object. An object at infinity gives an image at . This is exactly her old far point. So she sees objects at infinity clearly, and the new far point is infinity.
Step 3. The nearest object. The image must be at her old near point, . We want , so . So .
Answer: . The nearest object is away. The far point is infinity.
What about Tomas? Tomas is wrong. The near point moves farther away, from to . A concave lens makes a virtual image that is closer to it than the object. The image must stay at or more from the eye, so the object must be farther than . Her new range of clear vision is to infinity.
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