A lens is made of glass of refractive index 1.50. If both the surfaces are convex and the radii of curvatures are 10 cm and 20 cm, then the focal length of this lens is

Question

Quizplus · Accepted Answer

Using the thin lens formula, we have:
$\frac{1}{f}=(n-1)[\frac{1}{R_1}-\frac{1}{R_2}]$
Where $n$ is the refractive index of the lens, $R_1$ and $R_2$ are the radii of curvature of the two surfaces of the lens, and $f$ is the focal length of the lens.

Substituting the given values, we get:
$\frac{1}{f}=(1.50-1)[\frac{1}{-10 cm}-\frac{1}{20 cm}]$
$\frac{1}{f}=(0.50)[-\frac{3}{20}]	ext{ cm}^{-1}$
$\frac{1}{f}=-\frac{3}{40}	ext{ cm}^{-1}$
$f=-\frac{40}{3}	ext{ cm}=-13.3	ext{ cm}$

The negative sign indicates that the lens is a converging lens (i.e. convex on both sides), which is consistent with the given information. Therefore, the best choice is B.

A Lens Is Made of Glass of Refractive Index 1