PhysicsLAB: Determining the Focal Length of a Converging Lens

Introduction

This lab will determine the focal length of a given lens by using an optical bench to make measurements of object and image distances. In addition, you will be asked to make other observations that further your knowledge of properties of your lens.

Part I: Determining the Experimental Focal Length of your Lens

1. Measure the diameter of the quarter (object, h_o) and record below.

2. Place your quarter (object) and lens so the diameter of the image the quarter on the screen is less then 1.5 cm. Make sure that the image is brought into sharp focus.

3. Measure the distance between the object and the lens (d_o). Record the value in the table below.

4. Measure the distance between the lens and the screen (d_i). Record the value in the table below.

5. Calculate the focal length from the above measured values using the thin lens formula (1/f = 1/d_o + 1/d_i) and record the value in the table below.

6. Repeat steps 2-5 for image diameter equal to 2.5 cm and greater then 5.0 cm.

h_o = ____ cm

image height
criteria

measured
image height

object
distance

image
distance

focal
length

h_i < 1.5 cm

h_i = 2.5 cm

h_i > 5.0 cm

What was your average focal length (f_ave) in cm?

Part II: Affect of Covering the Lens:

Using the last setup on your optical bench (h_i > 5.0 cm) take a card and slowly cover the lens while watching the affect of the image.

Describe what happens to the image (what part of the image disappears; what happens to the brightness of the image; at what point are you unable to see the image?)

Part III: Scaled Lens Diagrams

Using your measured object height (h_o) and your average focal length (f_ave) along with each trial's measured object distance (d_o), draw a ray diagram for each trial.

Once you locate and construct each image, measure your diagram's scaled image distance (d_i) and scaled image height (h_i).

Trial #1: h_i < 1.5 cm

d_i = ___ cm

h_i = ___ cm

Trial #2: h_i = 2.5 cm

d_i = ___ cm

h_i = ___ cm

Trial #3: h_i > 5.0 cm

d_i = ___ cm

h_i = ___ cm

Based on these diagrams, how good was your average focal length (f_ave)? Why?

Part IV: Magnification of the Image

Notice from the following diagram that the geometry of similar triangles shows that:

h_o/ d_o = h_i/ d_i

Rearranging these ratios gives us the expressions:

|d_i/ d_o| = |h_i/ h_o|

These are two alternative ways to determine the magnification of an image.

Using the measured values in the table from Part I, calculate the magnification for each trial.

Trial

h_i/ h_o

d_i/ d_o

h_i < 1.5 cm

h_i = 2.5 cm

h_i > 5.0 cm

Based on this information about magnification, which trial was the best? Explain.

Part V: Images within the Focal Length

Take your lens and place it on the candle printed on your paper below:

Slowly lift the lens above to candle printed on your paper while looking through the lens, until you reach the focal length.

What happens to the image as you look through the lens when you lift the lens off the paper?

Could you project this image that you see through the lens? Why?

Describe what you see when you have lifted the lens the focal length above the paper?

Part VI: Determining the Lens Position

1. Ask your lab instructor for the distance between your object (d_o) and your screen (d_i) and record the value below. You will be asked to turn in your lens to the instructor.

d_o + d_i = ___ cm

2a. Using your average focal length (f_ave), calculate the required distance that the lens should be placed from the object (d_o) to achieve your required separation.

d_o = ___ cm

2b. Which of the following magnifications are you expecting for this image?

reducedthe same size as the objectenlarged

3. Request your lens back from your lab instructor. In the presence of your instructor, place the lens on to the optical bench and observe the clarity of your image. Then re-position the lens so that the image is brought in to as sharp a focus as possible. Measure the final "best" distance between the object and the lens (d_o). Record the measured value below.

4. Determine the percent error between your experimental predicted value and the actual measured value.