Lab & Pre-lab #11

Name: 

Lab Partners: 

Date: 

Pre-Lab Assignment: 

Lenses and Images 

(Due at the beginning of lab) 

Directions: Read over the lab handout and then answer the following questions about the 

procedures. 

Question 1 What is your prediction 1.1 

Question 2 The relation between the position of the image and object for a thin lens is given 

by the thin lens equation: 

1 

d 0 

+ 1 d i 

= 1 f 

where f is the focal length of the lens. Using the fact that 1 divided by a very large number is 

nearly 0, show that the thin lens equation predicts that an object located at the focal point gives 

an image that is infinitely far away, that is, when d i is very large, d o = f. 

Question 3 Below is a scale drawing of a lens with a focal length f = 15 cm with an object 

located a distance d o = 20 cm to the left of the lens. The circles mark the locations of the focal 

points, 15 cm to either side of the lens. In the next activity you will set up an object 20 cm 

from a 15 cm focal length lens, and locate the position at which the image is formed. Make a 

ray diagram for this situation, following the steps given in Activity 1.2. Use the ray diagram to 

determine the distance from the lens to the image that will be formed. 

Object 

f 

f 

PHYS-204: Physics II Laboratory 

i

Name: 

Lab Partners: 

Date: 

Lenses and Images 

Objectives 

• To understand what is meant by the focal point of a lens. 

• To understand the relationship between the object distance, the image distance and the 

focal length of a lens. 

• To understand the types of images formed by a lens. 

Overview 

Lenses are used in many devices that we use everyday-they are essential for the operation of 

cameras and projectors. Lenses are needed for devices such as microscopes to magnify small 

objects so that we can see them. 

In the previous lab you studied the refraction of light rays by lenses. In this experiment we 

will continue this investigation by observing images formed by lenses in various arrangements, 

and determining how the positions and sizes of these images are related to the positions and 

sizes of the object. 

These labs have been adapted from the Real Time Physics Active Learning Laboratories [1]. 

The goals, guiding principles and procedures of these labs closely parallel the implementations 

found in the work of those authors [1, 2, 3]. 

Investigation 1: 

Images formed by a convex lens 

Every lens has two focal points. The importance of these points is that all light rays reaching 

the lens coming from a very distant object (ideally, infinitely far away) will be focused at a 

focal point, as in Fig. 1. 

The focal length is the distance from the center of the lens to a focal point. The focal length 

depends on how the lens is made. The curvature of the surfaces of the lens determines the focal 

length. 

Prediction 1.1 Will a lens whose surfaces have very little curvature have a smaller or larger 

focal length than one for which the surfaces have greater curvature 

To carry out this activity, you will need the following: 

• One 15 cm focal length convex lens. 

• One 30 cm focal length convex lens. 

• optical bench. 

PHYS-204: Physics II Laboratory 1

Lenses and Images v 0.1 

Focal Point 

f 

f 

Focal Length 

Figure 1: Parallel light rays converge at the focal point. 

• light source. 

• F-diaphragm. 

• lens holders. 

• white projection screen. 

• meter stick. 

Activity 1.1: Focal Lengths of Convex Lenses 

Step 1: Examine the two convex lenses. The lenses have their focal length marked on them. 

One should have a focal length of +15 cm, the other +30 cm. Note which has the more 

sharply curved surfaces.. 

Question 1.1 To make a lens with shorter focal length, should the surfaces have greater 

or less curvature than for a longer focal length lens Which lens would you say a lens is 

more “powerful” if it has a shorter focal length, or a longer focal length 

Light rays which start from an object located at the focal point follow the paths shown 

in Fig. 1, but in the reverse direction. These rays diverge from the focal point, enter the 

lens and come out of the lens parallel to each other. This situation is depicted in Fig. 2. 

Step 2: Mount the light source and F-diaphragm at one end of your optical bench. The F- 

diaphragm should be right up against the light source, as in Fig. 3. This F-diaphragm 

provides the ”object in each of our optical systems. 



Light Source 

at Focal Point 

f 

Focal Length 

Figure 2: Light rays starting at the focal point come out parallel 

lamp 

Figure 3: Arrangement of light source, F-diaphragm, and lens. 

Step 3: Mount the 15 cm lens on the optical bench using a lens holder. Do not tighten the 

mounting screw on the holder-leave it loose so that you can slide the lens back and forth. 

Step 4: Turn the optical bench so that the light is directed towards the wall on the far side of 

the room. The distance to the other side of the room is very large compared to the focal 

length, so this can be considered to be essentially infinity. 

Step 5: Turn on the light source, and slide the lens holder back and forth until a sharp image 

is formed on the opposite wall. When you have a sharp image formed far away, the object 

must be located at the focal point. Thus the distance from the lens to the F-diaphragm 

should be just the focal length. Measure this distance with the meter stick, and record it 

as the measured focal length below. Also record the focal length marked on the lens. 

Measured focal length cm. Marked focal length cm 

Question 1.2 Does your measured focal length agree with the value marked on the lens. 



Step 6: Replace the 15 cm lens with the 30 cm lens. Again adjust the position of the lens 

to get a clear image on the opposite wall. Measure the distance from the lens to the 

F-diaphragm, and record it, together with the value of the focal length marked on the 

lens. 

Measured focal length cm. Marked focal length cm 

Question 1.3 Does your measured focal length agree with the value marked on the lens. 

Image 

Object 

f 

f 

Figure 4: Many light rays converging at one point to form an image. 

Activity 1.2: 

Locating an Image Using a Ray Diagram 

We will now examine what determines the location of an image formed by the lens when the 

object is not at the focal point. Recall from last week’s lab how an image is formed. The lens 

deflects the rays of light that come from one point in the object so that they converge and all 

cross at some point. That point is where the image is formed, as in Fig. 4. Out of all these 

rays, there are three whose paths are easy to determine. These are shown in Fig. 5. To locate 

these rays it is only necessary to know the locations of the object, lens, and focal points. You 

should do this activity before coming to the lab, as part of the pre-lab assignment. 

Fig. 6 is a scale drawing of a lens with a focal length f = 15cm with an object located a 

distance do = 20cm to the left of the lens. The circles mark the locations of the focal points, 

15cm to either side of the lens. In the next activity you will set up an object 20cm from a 15cm 

focal length lens, and locate the position at which the image is formed. 

Step 1: Use a ruler with a centimeter scale to measure the distance between from one focal 

point to the other in Fig. 6 of your lab handout. Using the fact the these two points 

represent points which are actually 30cm apart, work out the scale of the drawing - that 



a 

b 

Image 

Object 

f 

f 

c 

Figure 5: The Principle rays that are sufficient to locate an image. Ray (a) starts parallel to 

the axis and is deflected through the opposite focal point. Ray (b) Goes through the center of 

the lens where it is not deflected. Ray (c) goes from the object through the first focal point, 

and is then deflected so that it emerges parallel to the axis. The tip of the arrow of the image 

is located where these rays cross. Any two of these three are sufficient to find the location of 

the image. 

is the number of centimeters in the actual physical arrangement corresponds to 1cm in 

the drawing. 

Scale factor: cm per 1 cm in the drawing. 

Step 2: Draw two of the principle rays on the scale drawing (use a ruler to make sure they are 

straight and go through the right points). Draw an arrow corresponding to the image, 

with the tip of the arrow located where the rays cross. You should then draw the third 

principle ray - it should intersect the others right at the tip of the arrow. If it is way off, 

try redoing your drawing more carefully. 

Step 3: Measure the distance from the center of the lens to the image of the arrow on your 

drawing. Using the scale factor you determined in step 1, convert this to the actual 

distance from the lens that the image will be formed. 

Measured distance to image in the ray diagram 

cm 

Actual distance to the image (previous answer times the scale factor): 

d i = 

cm 

Step 4: Measure the height of the image and the object, and record them. Then calculate 

their ratio, h i /h o . Then calculate the ratio of the image and object distances, d i /d o . 

h i = cm h o = cm 

h i /h o = d i /d o = 



Object 

f 

f 

Figure 6: Scale drawing with f = 15 cm, and d o = 20 cm. 

Question 1.4 Is the ratio of the heights of the image and object nearly equal to the ratio of 

their distances Identify triangles in your ray diagram that show that these ratios must be equal, 

according to the theorem from geometry that the ratios of sides in similar triangles are equal. 

Activity 1.3: Locating the Image Experimentally 

Step 1: Place the white screen in a holder, and mount it at the end of the optical bench 

opposite the light source. When the screen is located where the light rays cross to form 

an image, the image will be projected clearly on the screen. 

Step 2: Remove the 30 cm lens if it is still mounted on the optical bench, and replace it with 

the 15 cm lens. 

Step 3: Move the lens holder to make the distance from the F-diaphragm to the lens d o = 20 

cm, as in the ray diagram in Activity 1.2. 

Step 4: With the light source on, slide the screen toward the lens until you locate the distance 

at which a clear image is formed. Measure the distance from the lens to the image, d i ,.with 

a meter stick. 

d i = cm. 

Question 1.5 Compare the image distance you have just measured with the image distance 

determined with your ray diagram in Activity 1.2. In making this comparison, take 

into account how accurately you could measure the distance from the lens to the object, 

and lens to the image. Also, try to estimate how accurately you could determine the image 

distance with the ray diagram. If the difference between your measured value and the one 

determined from the ray diagram are not larger than these estimated amounts, then you 

can say that the measured and theoretical values agree within experimental error. 



Step 5: Measure the height of the image, h i , and the height of the object, h o , and record these. 

Also note whether the object is inverted or erect. Then calculate the ratios of the image 

and object heights, and the image and object distances. 

measured: h i = cm measured: h o = cm 

measured: h i /h o = measured: d i /d o = 

Question 1.6 Is the ratio of the measured heights of the image and object nearly equal 

to the ratio of the measured distances Again, discuss the accuracy with which you could 

measure these quantities to draw a fair conclusion about their equality. 

There is an algebraic equation that relates the object distance, d 0 , (the distance from 

the lens to the object), the image distance, d i , (distance from lens to the position of the 

image), and the focal length, f, of the lens. This relationship involves the power of the 

lens, which is inversely proportional to the focal length (shorter focal length means greater 

power). 

1 

+ 1 = 1 thin lens formula 

d o d i f 

. 

Question 1.7 Using the formula above calculate the image distance given that f = 15cm, 

and d o = 20cm. Compare this with your measured value, again taking into account the 

precision in your measurement of the image and object distances. 

Measured: d i = 

cm. 

Prediction 1.2 What will happen if the distance from the lens to the object is increased 

Will the image distance get shorter or longer Will the image get larger or smaller To 

make this prediction, make a ray diagram with the object farther from the lens than the 

previous one. A scale drawing is provided in Fig. 7. 

Now test your predictions. 

Step 6: Move the lens so that it is at least 30cm from the F-diaphragm. 

Step 7: Move the white screen until you find a position at which a clear image is formed. 

Step 8: Measure the object and image distances, and the height of the object and image. 

Record the measurements below. 

d i = cm d o = cm 

h i = cm h o = cm 



Object 

f 

f 

Figure 7: Scale drawing with f = 15 cm, and d o = 30 cm. 

Question 1.8 Do these measurements agree with your Prediction 1.2 

Question 1.9 Calculate the theoretical image distance for the object distance you have measured, 

using the thin lens formula, 

1/d o + 1/d i = 1/f 

Calculated: d i = 

cm 

Also calculate the ratios of the image and object sizes, and the image and object distances: 

h i /h o = d i /d o = 

Discuss the comparison between the calculated and measured values, taking into account the 

precision of your measurements. 

Activity 1.4: Images in Space 

So far we have been observing images by projecting them on a wall or a screen. This allows us 

to locate the position and measure the size of our image with fairly accurately. But realize that 

an image is formed wherever multiple rays of light that started at one point cross, whether or 

not there is something to project the image on or not. In this activity we will observe images 

that are not projected on a screen. 

Step 1: Keep the screen, lens and F-diaphragm in the position they were in at the end of the 

previous activity. The screen should be at the position where a clear image is formed on 

it. Either note the position of the screen on the optical bench, or place something on the 

table to mark the screen’s position. . 



Step 2: Remove the screen. Now look toward the lens from a position about two feet beyond 

where the screen had been located. Look for the image of the ”F” floating in front of the 

lens. It will be inverted, just like the image that had been projected on the screen. It 

should appear to be in the same position where the screen had been. Each member of 

your group should make this observation. 

lamp 

former screen position 

eye 

Figure 8: Locating a real image with your eye, using parallax 

Step 3: To locate the position of this image in space more accurately, have one member of the 

group hold their finger above the position at which the screen had been located, as in the 

figure above. Hold the finger high enough that it does not block the light coming through 

the lens. Another member should then look at the image while moving their head left and 

right a small amount.. As you do this, the image will appear to move relative to objects 

in the background. But the image and the finger will appear to move together if they are 

the same distance from your eye.. (This phenomenon is called parallax – it is how we tell 

distances to objects with our eyes.) 

Question 1.10 Was the image you observed in space at nearly the same location at which 

the image had been formed on the screen 

Question 1.11 Did the image you observed in space have the same characteristics as the 

one projected on the screen, that is, was it about the same size Were both inverted 

Activity 1.5: Observing a virtual image 

In last weeks laboratory you discovered that when an object is too close to a lens, the 

light rays coming out of the lens diverge, as if they were coming from some single point 



behind the lens. In this case it is not possible to project a clear image on a screen. But 

we can still observe this image using the technique developed in activity 1.4. 

Question 1.12 Using the thin lens formula, calculate where an image will be formed if 

the object is 10cm from a lens of focal length 15cm. 

d i = 

cm 

Question 1.13 What is the meaning of the minus sign in your answer. 

Step 4: Move your lens so that it is 15cm from the F-diaphragm. 

Step 5: Look toward the lens. This time you should see an image that appears to be behind 

the lens. You may note be able to see the entire F at one time, since it will appear to be 

magnified. Have all members of your group make this observation. 

Question 1.14 Is the appearance of the image behind the lens consistent with your answer 

to Question 1.13 Is the image erect, or inverted. 

Step 6: Again have someone hold a finger above the position of the image-the person observing 

the image will have to give instructions to have the person move there finger until it 

appears to be at the same distance as the image. Once the finger is in the proper position, 

measure the distance from the lens to the finger. This is the measured image distance. 

measured d i = 

cm 

Question 1.15 Compare the measured and calculated image distances. Recognize that this 

method of measuring the distance is not as accurate as when the image was projected on a 

screen. 

This laboratory exercise has been adapted from the references below. 



lamp 

eye 

Figure 9: Locating a virtual image with your eye, using parallax. 

The hand shows the location of a virtual image of the F-diaphragm. 

References 

[1] David R. Sokoloff, Priscilla W. Laws, Ronald K. Thornton, and et.al. Real Time Physics, 

Active Learning Laboratories, Module 3: Electric Circuits. John Wiley & Sons, Inc., New 

York, NY, 1st edition, 2004. 

[2] Priscilla W. Laws. Workshop Physics Activity Guide, Module 4: Electricity and Magnetism. 

John Wiley & Sons, Inc., New York, NY, 1st edition, 2004. 

[3] Lilian C. McDermott, et.al. Physics by Inquiry, Volumes I & II. John Wiley & Sons, Inc., 

New York, NY, 1st edition, 1996.

Lab & Pre-lab #11

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