Chapter 24, Problem 65PP

Refraction of liquids. The focal length of a mirror can be determined entirely from the shape of the mirror. In contrast, to determine the focal length of a lens, we must know both the shape of the lens and its index of refraction—as well as the index of refraction of the surrounding medium. For instance, when a thin lens is immersed in a liquid, we must modify the thin-lens equation to take into account the refractive properties of the surrounding liquid:

$\frac{1}{f}=\left(\frac{n}{n_{\text{liq}}}-1\right)\left(\frac{1}{R_1}-\frac{2}{R2}\right)$

where n_liq the index of refraction of the liquid and n is the index of refraction of the glass.

65. In air, a particular person sees clearly when wearing eyeglasses that have glass lenses with a specific radius of curvature. To see clearly when scuba diving, this person wants to have her optometrist make new lenses that can be mounted in front of her scuba mask so that the lenses are surrounded by water. Which of the following is true if the new lenses are to have the same focal length in water as the original lenses do in air? The new lenses need to

1. A.    have a larger radius of curvature compared to the original lenses.
2. B.     have a smaller radius of curvature compared to the original lenses.
3. C.     have the same radius of curvature as the original lenses.
4. D.    be flat pieces of glass.