# Focusing LED using a Fresnel lens at different distances

Simple setup: A Red LED in front of a small fresnel loupe/lens (credit card size). Using a screw I can adjust the distance between the LED and the lens. The LED is centered with regard to the lens.

My question: I pointed my assembly at a wall 1 meter away and adjusted the distance so that the resulting spot on the wall has the smallest diameter (increasing and decreasing the distance at this point results in the spot to grow and get blurry). Then I aimed at a different wall which is about 4 meters away and the spot got bigger - as expected. However, I was surprised to find that, with the different distance to the wall, adjusting the distance between LED and lens leads to a more focused spot.

What is the reason for this? Why and how does the distance between LED/lens and the wall I am pointing at matter?

A picture for the 3 cases: 1m (diameter 3cm, focus), then turned at 4m (12cm, out of focus), then distance adjusted (10cm, again focus)

• Hello, and welcome to Stack Exchange. What are the two spot sizes? And, pictures of the two could really help. Commented Sep 16, 2017 at 12:40
• @DanielGriscom I uploaded the pictures and measured the diameters. Commented Sep 16, 2017 at 13:11
• My original read was that you were surprised to get a smaller spot at 4m than at 1m. Now, I'm thinking you were surprised that you had to change the LED-lens distance with a changed lens-wall distance. Which is it? (The latter is due to simple optics.) Commented Sep 16, 2017 at 13:18
• Yes, I am surprised that I have to change the lens-LED distance with a changed lens-wall distance - would really appreciate clarification on that. Doesn't focus mean that you send out the narrowest beam possible? Commented Sep 16, 2017 at 13:22
• Is this just an application of the lens formula, $\frac 1 u + \frac 1 v=\frac 1f$ with $f$ the focal length of the lens, in that as you change the image distance $v$ you then have to change the object distance $u$ to get the image in focus? Commented Sep 16, 2017 at 15:06

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