A convex refracting surface has a radius of 12 cm.Light is incident in air (n = 1)and refracted into a medium with an index of refraction of 2.To obtain light with rays parallel to the central axis after refraction a point source should be placed on the axis:
A)3 cm from the surface
B)6 cm from the surface
C)12 cm from the surface
D)18 cm from the surface
E)24 cm from the surface

Question

Quizplus · Accepted Answer

This problem requires the use of the lens maker's equation: $\frac{1}{f}=(n-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$, where $f$ is the focal length of the lens, $n$ is the index of refraction of the medium the light enters after refraction, $R_1$ is the radius of curvature of the left/first surface of the lens, and $R_2$ is the radius of curvature of the right/second surface of the lens. We are given $n=2$ and $R_1 = \infty$ since the light enters from air, which is much less dense than the lens material. We are also given $R_2 = -12$ cm since the surface is convex (curvature is outward) and $R_2$ is negative. Plugging in these values gives:

$\frac{1}{f}=(2-1)\left(\frac{1}{\infty}-\frac{1}{-12}\right) \Rightarrow f=-12$ cm

We want to find the distance from the surface of the point source that will produce parallel rays after refraction. This is the same distance as the focal length, so the answer is C) 12 cm from the surface.

A Convex Refracting Surface Has a Radius of 12 Cm