A number of factors play a role in determining the focal length of

a lens. First and foremost is the shape of the lens. As a general rule,

a lens that is thicker in the middle will converge light, a lens that is

thinner in the middle will diverge light. Another important factor is the index of refraction of the lens

material, $n_{\text { lens. }}$ For example, imagine comparing two lenses with

identical shapes but made of different materials. The lens with the larger index of refraction bends light more, bringing it to a focus in a

shorter distance. As a result, a larger index of refraction implies a focal

length with a smaller magnitude. In fact, the focal length of a lens

surrounded by air $(n=1)$ is given by the lens maker's formula:

$$

\frac{1}{f_{\text { in air }}}=\left(n_{\text { lens }}-1\right)\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right)

$$

A lens is not always surrounded by air, however. More generally, the fluid in which the lens is immersed may have an index of

refraction given by $n_{\text { finid }} .$ In this case, the focal length is given by

$$

\frac{1}{f_{\text { in fluid }}}=\left(\frac{n_{\text { lens }}-n_{\text { fluid }}}{n_{\text { fluid }}}\right)\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right)

$$

It follows, then, that the focal lengths of a lens surrounded by air

or by a general fluid are related by

$$

f_{\text { in fluid }}=\left[\frac{\left(n_{\text { lens }}-1\right) n_{\text { fluid }}}{n_{\text { lens }}-n_{\text { fluid }}}\right] f_{\text { in air }}

$$

This relation shows that the surrounding fluid can change the

magnitude of the focal length, or even cause it to become infinite.

The fluid can also change the sign of the focal length, which determines whether the lens is diverging or converging.

Calculate the focal length of a lens in water, given that the index of refraction of the lens is $n_{\text { lens }}=1.52$ and its focal length

in air is 25.0 $\mathrm{cm} .$ (Refer to Table $26-2 . )$

$\begin{array}{ll}{\text { A. } 57.8 \mathrm{cm}} & {\text { B. } 66.0 \mathrm{cm}} \\ {\text { C. } 91.0 \mathrm{cm}} & {\text { D. } 104 \mathrm{cm}}\end{array}$