PART I - The Thin Lens Equation
![](data:image/png;base64,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)
• Move the object so that the eraser is on the optical axis.
• From the green control box, select Many Rays.
The Many Rays setting allows you to see a depiction of light being diffusively scattered from the point of the pencil. Several of these scattered rays intersect the lens. Because the lens is curved, each ray encounters the surface of the lens at a slightly different angel. Snell's Law tells us that each light ray is going to be bent at a slightly different angle. Here is where it gets interesting. The bent rays intersect each other at a location called the focal point of the lens.
The relationship between the object distance (p), the image distance (q), and the focal length (f) is captured by the thin lens equation
• Select the ruler from the green control panel.
![](data:image/png;base64,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)
• Choose any Radius of Curvature other than the default 0.8 m.
• Move the object to any position on the optical axis outside the focal length (e.g., beyond the "x"),
• Measure the image and object distances.
• Repeat 5 times.
In your laboratory notebook, create a table that contains the focal length, object distance, and measured image distance. In two additional columns, include the image distance calculated from the thin lens equations above and the difference between the two image distances. Also write a short paragraph describing whether or not your data and analysis supports or fails to support the thin lens equation.