# Converging Lenses Isaac Ilivicky and Noam Kantor.

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Converging Lenses Isaac Ilivicky and Noam Kantor

Purpose The purpose of this lab was to investigate the relationship between the object distance and the image distance for real images produced by a converging thin lens. In order to do this, we specifically analyzed the relationships between: Image Distance vs. Object Distance Image Height vs. Object distance

Hypothesis As the object distance increases, the image distance decreases. As the object distance increases, the image height decreases.

Apparatus A converging thin lens Multiple rails preferably with an attached scale (meter sticks on the sides) A light source (light bulb) The Object (an opaque sheet with a symbol of some sort cut out in the center, ours happened to be an “L”) A screen where the image will be shown (multiple sizes will most likely be necessary) A computer with LoggerPro or an organized data table of some sort Time, patience, and some humor

Procedure 1. Measure the focal length by pointing lens at an object very far away. The prime object in our physics explorations has been a power pole across the highway. Adjust the position of the screen until the object is very “in focus.” The distance from the lens to the screen is the focal length of the lens. 2. In a dark laboratory, start with the object 15 focal lengths away form the lens. On the opposite side of the lens from the object, move the screen until you find a well-focused image. Record the distance from the lens is known as the object distance. 3. Change the object distance in increments of approximately one focal length (rounded to the nearest 5.0 cm) until you reach a distance of 3 focal lengths away from the lens, recording the image distance and image height each time. Our suggestion is that in order to measure the same values without having to move the object every time (which with our apparatus was part of the light source), it is easier to move the lens and the screen. 4. When you are 3 focal lengths away from the lens, reduce the distance increment to 5.0 cm. 5. When you are 2 focal lengths away, reduce the distance increment to 1.0 cm until you reach an object distance of 1.0 cm less than 1 focal length away. 6. Another reminder; at every position, remember to record the object distance, image distance, and the image height. 7. Plot image distance vs. object distance and image height vs. object distance, and proceed with the analysis.

Diagram Credit to the UCLA physics department, however, due to current situations, GO TROJANS!

Raw Data

Raw Graph Image Distance vs. Object Distance

Manipulated Graph

Linearized Graph

Mathematical Analysis Image Distance vs. Object Distance

Raw Graph

Manipulated Graph

Linearized Graph

Mathematical Analysis Image Distance vs. Object Distance

Error Sources It was exceedingly difficult to tell whether an image was focused at a given position when the image distance was large because the image was dim anyways. So it was hard to differentiate between dimness and being out of focus.

Error Values 7.9% Experiment 1:Experiment 2: 7.9%

Ray Diagram!

Error Sources The scale for the height only went to the nearest 2mm, so there was a large amount of estimation. At large object distances, the image was very small, and so this small scale was difficult to read.

Mathematical Model

Geometric Model http://www.physicsclassroom.com/Class/refrn/u14l5da5.gif