## Fundamentals of Physics Extended (10th Edition)

$2.00$
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: $\frac{n_1}{\infty}+\frac{n_2}{i}=\frac{n_2-n_1}{r}$ $\frac{n_2}{i}=\frac{n_2-n_1}{r}$ Solving 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 is twice the radius of the sphere ($i=2r$) Using this information with the equation, we obtain: $n_2=1.00(1-\frac{r}{2r})^{-1}$ $n_2=1.00(1-\frac{1}{2})^{-1}$ $n_2=2.00$