# Beam Expander Example

## Example 3: Beam expanders

Say you're building a microscope and you want to expand the coverage of light that is illuminating your sample. You decide you want to build a beam expander to accomplish this. Assume that the incident light is collimated and you want the resulting light from your beam expander to also be collimated. Come up with two ways to make a beam expander using only two lenses each time--one way with two converging lenses, and another way with one converging and one diverging lens. For each system, answer the following questions:

A) At what distance do the two lenses have to be for the light to still be collimated when exiting the second lens?

B) How much have you magnified the beam after the second lens?

C) Is the final image inverted or upright?

D) What happens if you switch the order of the lenses?

**Method 1: Two converging lenses**

We will only set up the diagram here. The rest will be left to you to work out. Remember that a good practice is to put the curved side of the lens toward the collimated light.

**Method 2: One diverging lens and one converging lens**

Here, $ f_1<0 $ and $ f_2>0 $. Also, $ f_2>|f_1| $. You will see why this is the case.

A) At what distance do the two lenses have to be for the light to still be collimated when exiting the second lens?

B) How much have you magnified the beam after the second lens?

C) Is the final image inverted or upright?

D) What happens if you switch the order of the lenses?