Converging Lenses Graphical Analysis By Chris Cho and Dan Fan

Purpose  Determine the relationship between object distance and image distance for real images produced by a converging thin lens.  Determine the relationship between object height and image height.

Hypothesis  Object distance is inversely proportional to image distance.  Object height is directly proportional to image height.

Materials  Cart Track  White Screen  Converging Lens  Light Source  Cut-out Arrows of Various Sizes on Cardboard  Cut-out Number “4” on Cardboard  Meter Stick  Chris’ Mom

To Find the Focus Obtaining the Focus length. 1. Place the screen at a given length on the cart track so that there is enough room to place the converging lens on the side that points toward the window. 2. Point the apparatus toward the window and locate a specific object in the far distance. 3. Observe the image on the screen and focus the image by adjusting the distance between the screen and the lens. 4. When the image is “perfectly” focused, measure the distance from the screen to the lens and this will be the focus length.

Focus Diagram

General Lab Procedure 1. Start by placing the converging lens a total of 15 focal lengths away from the object (the distance between the lens and the object is the object distance). Adjust the screen so that the image becomes clear. (the distance between the screen and lens is the image distance. Shorten the object distance by 1 focal length increments and adjust the screen while measuring the image distance and object distance each time. Shorten the object distance by smaller increments once you approach a distance of 2 focal lengths. 2. Move the converging lens 1.5 focal lengths away from the object. Place a cut-out arrow in front of the light source and adjust the image distance until the projected image is clear. Measure both the real and the projected arrow’s length. Do the same with arrows of varying sizes. Repeat the same procedure with a 2.5 focal length object distance.

Distance Exploration Table

Image Distance vs Object Distance

Image Distance vs 1/ Object Distance

1/ Image Distance vs 1/ Object Distance

1/ Image Distance vs 1/ Object Distance Mathematical Analysis

Image Height vs Object Height Table

Image Height vs Object Height Graph

Image Height vs Object Height Analysis

Drawing Ray Diagrams  Drawing Ray Diagrams:  Draw a ray from a point on the object parallel to the principle axis to the center of the lens. Draw another line extending from that point through the foci on the opposite side of the image. (can be done because of the definition of focus)  Draw a second ray from that point through the point in which the principle axis intercepts the lens.  Draw a third ray through the focus to the lens. Draw another line extending from that point parallel to the principle axis.  The point of intersection is the corresponding image point to the original object point.

Ray Diagram (around 1.5 foci) 2ff f Object Image

Ray Diagram (around 2 foci) 2f f f Object Image

Ray Diagram (around 2.5 foci) 2f f f Object Image

Fin