Correcting Nearsightedness

You want this nearsighted person to be able to see very distant objects clearly. That means the spectacle lens must produce an image 30.0 cm from the eye for an object very far away. An image 30.0 cm from the eye will be 28.5 cm to the left of the spectacle lens (see Figure 26.6). Therefore, we must get $d_{\text{i}}=-\text{28.5 cm}$ when $d_{\text{o}}\approx \infty$. The image distance is negative, because it is on the same side of the spectacle as the object.

Since $d_{\text{i}}$ and $d_{\text{o}}$ are known, the power of the spectacle lens can be found using $P=\frac{1}{d_{\text{o}}}+\frac{1}{d_{\text{i}}}$ as written earlier:

Since $\text{1/}\infty \text{= 0}$, we obtain:

The negative power indicates a diverging (or concave) lens, as expected. The spectacle produces a case 3 image closer to the eye, where the person can see it. If you examine eyeglasses for nearsighted people, you will find the lenses are thinnest in the center. Additionally, if you examine a prescription for eyeglasses for nearsighted people, you will find that the prescribed power is negative and given in units of diopters.