A convex-concave thin lens is made with the radius of curvature of the convex surface being 25.0 cm and the concave surface 45.0 cm.If the glass used has index of refraction 1.500,what is the focal length of this lens?
A) -32.0 cm
B) 32.0 cm
C) 113 cm
D) 67.5 cm
E) -113 cm

Question

Quizplus · Accepted Answer

The formula for the focal length of a thin lens is given by:
$$\frac{1}{f}=(n-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$$
where $n$ is the refractive index of the lens material, $R_1$ is the radius of curvature of the first surface (convex here) and $R_2$ is the radius of curvature of the second surface (concave here).
Substituting the given values in the above equation, we get:
$$\frac{1}{f}=(1.500-1)\left(\frac{1}{0.25}-\frac{1}{-0.45}\right)$$
Solving the above equation, we get $f=113$ cm. Therefore, the correct choice is C.

A Convex-Concave Thin Lens Is Made with the Radius of Curvature