Experiment 28

Real Images and Focal Lengths of Lenses

Objectives

To use the magnification of real images to find the focal length of both converging and diverging lenses.

Introduction

The thin lens formula and the formula for magnification by a lens are

respectively where o is the object distance, i is the image distance, f is the focal length, and M is the magnification.  Note that if the object is at infinity, i = f.

The focal length is positive for a converging lens and negative for a diverging lens.  o is positive if it is on the side of the lens from which the light comes and i is positive if it is on the side of the lens away from the source of the light.

Procedure

Measure f for the converging lens by finding i for an object at infinity.  Place the converging lens between the screen and the object.  Focus the image by moving the screen and record the positions of the object, lense and screen.  Also measure the image and object heights.  Now place the diverging lens between the converging lens and the screen.  Move the screen to refocus the image and record the position of the diverging lens and the new screen position.  Calculate o for the diverging lens.  Also, measure the new image size.  Repeat this whole procedure for 5 more different values of o.  Try to get as wide a range of values of o as possible for both lenses.

Graphs and Calculations

Plot o vs. 1/M for each lens where M = -image size/object size and not the result from equation 2.  Using equations 1 and 2, we derive the prediction that

3)  o = f -f(1/M)

This equation is identically true assuming that equations 1 and 2 are correct.  We now check the validity of equation 2 against the "real" meaning of magnification, i.e., changes in image size (eq. 2 is in terms of distance rather than size).  Plot a least squares fit for this data. The slope and intercept should both give values of f for both lenses if equation 3 (and equation 1 and 2) is correct.

Quote an average focal length for each lens plus or minus the average deviation of your values.  You should have 3 values of f for the converging lens and 2 for the diverging lens.