Question

A common optical instrument in a laser laboratory is a beam expander. One type of beam expander is shown in FIGURE P $35.29$. The parallel rays of a laser beam of width w1 enter from the left.

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

b. What is the width w2 of the exiting laser beam?

Short answer

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

b. The width w2 of the exiting laser beam is$w_2=\frac{f_2}{\left|f_1\right|}{w}_2$.

Step-by-step solution

Part (a) Step 1: Given Information.

We need to find out d's lens spacing a parallel leaser beam exit from the right.

Part (b) Step 2: Diagram explanation.

We see the following from the picture which is given below:

$d=f_2-\left|f_1\right|$

If $f_1<0$, which is equivalent to:

$d=f_2+f_1$

Here, $d$is the distance between lens, $f_{1}and{f}_2$is the focal length of the first and second lens respectively.

Part(b) Step 1: Given Information.

We need to find out the width $w_2$leaser beam.

Part (b) Step 2: Explanation.

As we know that to find width $w_2$

Triangles a from above picture, we can get the values for $w_2$:

$$\begin{gathered} \frac{w_1}{\left|f_1\right|}=\frac{w_2}{f_2} \\ \Rightarrow w_2=\frac{f_2}{\left|f_1\right|}{w}_1 \end{gathered}$$

Here, $w_{1}and{w}_2$is the width of first lens and second lens and $f_1,f_2$are the focal length of first and second lens respectively.

So, if is $f_2>f_1$and our conclusion show that is $w_2>w_1$.