Fundamentals of Physics Extended (10th Edition)

Published by Wiley

Chapter 34 - Images - Problems - Page 1039: 39b

Answer

It is not possible to focus the image at the center of the sphere.

Work Step by Step

First we consider equation (34-8): $\frac{n_1}{p}+\frac{n_2}{i}=\frac{n_2-n_1}{r}$ We note that the object distance is infinite ($p=\infty$), and obtain: $\frac{n_1}{\infty}+\frac{n_2}{i}=\frac{n_2-n_1}{r}$ $\frac{n_2}{i}=\frac{n_2-n_1}{r}$ Ssolving for the index of refraction of the sphere, $n_2$, we obtain: $n_2=n_1(1-\frac{r}{i})^{-1}$ We know the first index of refraction is that of air, so $n_1=1.00$ and the image distance must be equal to the radius for the image to appear at the center of the sphere ($i=r$) Using this information with the equation, we obtain: $n_2=1.00(1-\frac{r}{r})^{-1}$ $n_2=1.00(1-1)^{-1}$ $n_2\approx \infty$ This is not possible. There is no index of refraction that will focus the image at the center of the sphere.

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.