#### Question

Contact lenses are placed right on the eyeball, so the distance from the eye to an object (or image) is the same as the distance from the lens to that object (or image). A certain person can see distant objects well, but his near point is 45.0 cm from his eyes instead of the usual 25.0 cm. (a) Is this person nearsighted or farsighted? (b) What type of lens (converging or diverging) is needed to correct his vision? (c) If the correcting lenses will be contact lenses, what focal length lens is needed and what is its power in diopters?

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#### Step 1

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$\begin{gathered} {\text{Object - image relationship for (((thin lens))) :}} \\ \\ \frac{1}{s} + \frac{1}{{s'}} = \frac{1}{f} \\ \\ s \Rightarrow {\text{object distance from the lens, }} \\ {\text{s'}} \Rightarrow {\text{The image distance from the lens,}} \\ f \Rightarrow {\text{The focal length of the lens}}{\text{.}} \\ \\ s \to ( + ){\text{ in front of the lens, (}} - ){\text{ in the back of the lens,}} \\ s' \to ( + ){\text{ in the back of the lens, (}} - ){\text{ in front of the lens,}} \\ f \to ( + ){\text{ the lens is convergent, (}} - ){\text{ the lens is divergent}}{\text{.}} \\ \end{gathered}$

The sign rules for the variables in the equation:

1. Sign rule for the object distance (s): when the object is on the same side of the refracting surface as the incoming light, object distance s is positive; otherwise, it is negative.

2. Sign rule for the image distance (s′ dash): When the image is on the same side of the refracting surface as the outgoing light (the refracted light), image distance s′ is positive; otherwise, it is negative.

Note: the focal length depend on the curvature of the surfaces which forms the lens and depend on the material of the lens.

Apply: in most problems, we are asked to get the position of the image forming from the refracted rays through a certain lens by using the focal length of the lens and the position of the object. In other problems, we are given the position of the object and the image to get the focal length of a lens.

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