A converging lens with two convex surfaces has a front surface with radius of curvature of 10.0 cm;the back surface has radius of curvature of 30.0 cm,and the lens is made from material with an index of refraction of 2.50.What is the focal length of the lens?
A) −13.3 cm
B) 4.44 cm
C) 5.00 cm
D) 0.250 cm

Question

Quizplus · Accepted Answer

Using the thin lens equation $\frac{1}{f}=(n-1)(\frac{1}{R_1}-\frac{1}{R_2})$, with $n=2.50$, $R_1=10.0 	ext{ cm}$ and $R_2=-30.0 	ext{ cm}$ (since the back surface is convex), we can solve for $f$:
$$\frac{1}{f}=(2.50-1)(\frac{1}{10	ext{ cm}}-\frac{1}{-30 	ext{ cm}})=0.4	ext{ cm}^{-1}$$
$$\Rightarrow f=\frac{1}{0.4 	ext{ cm}^{-1}}=2.5 	ext{ cm}$$
Therefore, the focal length of the lens is 5.00 cm, which is answer choice C.

A Converging Lens with Two Convex Surfaces Has a Front