Question

A common optical instrument in a laser laboratory is a beam expander. one type of beam expander is shown in FIGURE P$35.28$.

a. For what lens spacing d does a parallel laser beam exit from

the right?

b. What is the width of the exiting laser beam?

Short answer

a. Lens spacing d does a parallel laser beam exit from the right $d=f_1+f_2$.

b. The width of the exiting laser beam is${\omega }_2=\frac{f_2}{f_1}{\omega }_1$.

Step-by-step solution

part(a) Step 1: Given information

We need to find what lens spacing d does a parallel laser beam exit from the right.

part(a) Step 2: Explanation

We find this distance as the sum of the focal length of the first lens and the focal length of the second lens:

$d=f_1+f_2$

part (b) step 1: Given Information

We need to find the width of the exiting laser beam.

part (b) step 2: Simplification

let us find width ${\omega }_2$,

$$\begin{gathered} \frac{{\omega }_2}{{\omega }_1}=\frac{f_2}{f_1} \\ {\omega }_2{f}_1={\omega }_1{f}_1 \\ {\omega }_2=\frac{f_2}{f_1}{\omega }_1 \end{gathered}$$

Here, ${\omega }_1$is the width of the first lens,${\omega }_2$is the width of the second lens, role="math" localid="1650107475863" $f_{1}and{f}_2$is the focal length of first lens and second lens.

part (b) step 3: Diagram