The Lens Makers Equation

The thin lens equation is not the whole story. You can and should play with all of the controls to see how they affect the focal point of the lens. The Lens Maker's

Equation takes into account both the index of refraction of the lens material and the curvature of the lens surface itself. The form we have below is a special case of a more general equation, in which the radii of curvature (R) of both lens surfaces are equal to each other.

Experimentally determine the relationship between the index of refraction and the radius of curvature for a constant focal length.

• Ensure that the ruler is still present in the simulation.

• Choose a radius of curvature other than the default value.

• Change the index of refraction by some small increment.

Observe the change in the position of the focal point. Use the slider bar to change the radius of curvature to bring the focal point back to its original position. Record both the index of refraction and the radius of curvature in your laboratory notebook. Repeat the process of changing both the index of refraction and the radius of curvature to obtain at least 10 data points. Plot your data on a scatter plot using your favorite spreadsheet program. What is the shape of this curve?

What happens to the required index of refraction as the radius becomes arbitrarily large or arbitrarily small? What conclusions can you draw about the material requirements of manufacturing small spherical lenses for use in personal electronic devices?