Question

Paraxial light rays approach a transparent sphere parallel to an optical axis passing through the center of the sphere. The rays come to a focus on the far surface of the sphere. What is the sphere’s index of refraction?

Short answer

The sphere’s index of refraction is equal to 2.00

Step-by-step solution

Step 1. Given information is :Paraxial light rays approach a transparent sphere parallel to an optical axis passing through the center of the sphere .

We need to calculate the sphere’s index of refraction

Step 2. Using formula that is for the convex surfaces

$$\begin{gathered} \frac{n_1}{s}+\frac{n_2}{s\text{'}}=\frac{n_2-n_1}{R} \\ s=\infty asthelightraysareParaxial \\ s\text{'}=2R \\ \frac{1}{\infty }+\frac{n}{2R}=\frac{n-1.00}{R} \\ \frac{n}{2R}=\frac{n-1.00}{R} \\ \frac{n}{2}=n-1.00 \\ n=2n-2.00 \\ n=2.00 \end{gathered}$$