Question 25.2: A Corrective Lens for Nearsightedness Goal Apply geometric o...
A Corrective Lens for Nearsightedness
Goal Apply geometric optics to correct nearsightedness.
Problem A particular nearsighted patient can’t see objects clearly when they are beyond 25 \mathrm{~cm} (the far point of the eye). (a) What focal length should the prescribed contact lens have to correct this problem? (b) Find the power of the lens, in diopters. Neglect the distance between the eye and the corrective lens.
Strategy The purpose of the lens in this instance is to take objects at infinity and create an image of them at the patient’s far point. Apply the thin-lens equation.
(a) Find the focal length of the corrective lens.
Apply the thin-lens equation for an object at infinity and image at 25.0 \mathrm{~cm} :
\begin{aligned} \frac{1}{p}+\frac{1}{q} & =\frac{1}{\infty}+\frac{1}{(-25.0 \mathrm{~cm})}=\frac{1}{f} \\ f & =-25.0 \mathrm{~cm} \end{aligned}
(b) Find the power of the lens in diopters:
\mathscr{P}=\frac{1}{f}=\frac{1}{-0.250 \mathrm{~m}}=-4.00 \text { diopters }
Remarks The focal length is negative, consistent with a diverging lens. Notice that the power is also negative and has the same numeric value as the sum on the left side of the thin-lens equation.