Chapter 35: Q. 29 (page 1018)

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?

Expert verified

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 $w_{2} = \frac{f_{2}}{|f_{1}|} w_{2}$ .

Step by step solution

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

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

$d = f_{2} - |f_{1}|$

If $f_{1} < 0$ , which is equivalent to:

$d = f_{2} + f_{1}$

Here, $d$ is the distance between lens, $f_{1} a n d f_{2}$ is the focal length of the first and second lens respectively.

We need to find out the width $w_{2}$ leaser beam.

As we know that to find width $w_{2}$

Triangles a from above picture, we can get the values for $w_{2}$ :

$\frac{w_{1}}{|f_{1}|} = \frac{w_{2}}{f_{2}} \Rightarrow w_{2} = \frac{f_{2}}{|f_{1}|} w_{1}$

Here, $w_{1} a n d w_{2}$ 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 $w_{2} > w_{1}$ .

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