Find the Focal Length of the Lens

A differentiated lab to test you skill with lab reports and geometric optics

Ray Tracing for LensesLenses are used to focus light and form images. There are a variety of possible types; we will consider only the symmetric ones, the double concave and the double convex.

Ray Tracing for LensesIf we think of a convex lens as consisting of prisms, we can see how light going through it converges at a focal point (assuming the lens is properly shaped).

Ray Tracing for Lenses

A concave lens can also be modeled by prisms:

Ray Tracing for LensesThese diagrams show the principal rays for both types of lenses:The three principal rays for lenses are similar to those for mirrors:• The P ray—or parallel ray—approaches the lens parallel to its axis.• The F ray is drawn toward (concave) or through (convex) the focal point.• The midpoint ray (M ray) goes through the middle of the lens. Assuming the lens is thin enough, it will not be deflected. This is the thin-lens approximation.

Ray Tracing for LensesThe convex lens forms different image types depending on where the object is located with respect to the focal point:

The Thin-Lens Equation

We derive the thin-lens equation in the same way we did the mirror equation, using these diagrams:

The Thin-Lens EquationSign conventions for thin lenses:

The focal Length can be found…

• Using the equations seen yesterday, your single objective is to find the focal length of the convex lens that is in your group’s optics kit. – The way you communicate your findings will dictate your

grade. There are several options to choose from.

The ‘D’ Option

• This option will earn you up to a ‘D’ or 69%• You provide an answer for the focal length

with the measurements and math. Minimal to no commentary on procedure and analysis.

f = 15.0cm

The ‘C’ Option

• This option will earn you up to a ‘C’ or 79%• You provide an answer for the focal length

with the measurements and math. A clear and concise commentary is given on the procedure and analysis used.

The ‘B’ Option

• This option will earn you up to a ‘B’ or 89%• You provide an answer for the focal length with

the measurements and math. A clear and concise commentary is given on the procedure and analysis used. More than one pair of object and image distances are used to calculate the focal length. Trial # do di f

1

2

3

The ‘A’ Option• This option will earn you up to an ‘A’ or

100%• You provide an answer for the focal

length with the measurements and math. A clear and concise commentary is given on the procedure and analysis used. More than one pair of object and image distances are used to calculate the focal length. A graph of the data is shown to depict how the focal length can be visualized as the slope of a function relating di and do.

The Options for the Lab

• Your single objective is to find the focal length of the convex lens that is in your group’s kit.

• All of the levels allow you to do this, and they all build on each other. – Ex: In order to do the B-

level, you must be able to do the C-level work

• Add a ray-diagram to any level for a polished look!

The options for this labD –LevelFind an answer for the focal length of your convex lens

C-levelFind a focal length and explain how you obtained it.

B-LevelUse multiple data points to minimize error in your focal point value.

A-LevelUse multiple data points and graphical analysis to minimize errors in results.