# Experiment: Imaging Properties of a Simple Lens

## Objective

In this experiment you will observe and measure the imaging properties of a simple lens.

## Apparatus

You will need a good lens (magnifying glass), a flashlight, a viewing screen (tri-folded white copy paper), a meter stick and perhaps some modeling clay to hold things in place. You will want to be able to set these items on a flat table about 1 meter wide in an area where the lighting can be dimmed.

## Background

The most basic optical imaging device is a simple lens like those found in a magnifying glass. These lenses have spherical surfaces and depend on the law of refraction for their image-forming properties. For the level of treatment in this experiment, the imaging properties of a lens is completely specified by giving the lens' focal length. The lens in a good magnifying glass will have a focal length typically around 5-15 cm.

The imaging capabilities of your lens can be demonstrated very nicely in a dark room with the picture from a TV set. Position the lens and screen about 2-3 meters from the TV. Adjust the distance between the lens and the screen until you get as sharp a picture as possible on the screen.

Question:
What do you notice about the image on the screen?

In the jargon of optics, the TV in this part of the experiment is called the object. The distance from the lens to the TV is called the object distance and given the symbol o. The picture on the screen is called the image. The distance from the lens to the image is called the image distance and given the symbol i. The focal length is given the symbol f.

Measure the image distance and record this on the data sheet.

Move the lens and screen an additional meter from the TV and repeat the measurements of the object and image distances recording your results on the data sheet.

Question:
Did you notice that the image distance did not change very much? Do you think this means the image distance doesn't depend on the object distance?

When the object distance is much much greater than the image distance, the image distance will be approximately the focal length of the lens. Thus, the image distances measured above are approximately the focal length of the lens.

Cut out a circular piece of opaque paper (black construction paper can be used) roughly the size of the face of the flashlight. Then fold the circle in half and cut out a wedge shape along the fold so that when the circle is unfolded the cutout will be in the shape of a long pointed triangle that is 1 cm from the pointed tip to the base. Put some tissue paper backing over the triangular hole and tape this (tissue side down) to the face of the flashlight. When the flashlight is turned on the brightly lit white triangle should make a good object suitable for image formation. For the rest of this experiment the triangle will be used as the object.

Begin by setting the object distance accurately to 20 cm. Adjust the position of the screen (image distance) to get a sharp image of the edges of the triangle. Record the object and image distances on the data sheet. Also measure and record the size of the image of the triangle (tip to base).

Repeat this procedure as you adjust the distance between the lens and flashlight (object distance) from 20 cm to about 70 cm in steps of 10 cm. Each time you will have to move the screen to reform the image of the triangle.

Question:
What happens to the size of the image as the object distance increases? What happens to the image distance?

Set the screen 50 cm from the lens (i=50 cm). This time, adjust the flashlight (object distance) to get a sharp image. Record again the object and image distances and the size of the image.

Graph:
Make a graph with image distance on the vertical axis vs. object distance on the horizontal axis. Just plot the data points. Do not connect them with lines.
Question:
Do the data points appear to lie on a smooth curve?

Try to draw a smooth curve through the data points. Remember, no measurements are ever perfect, so it is OK to let the curve miss the data points by a little.

Question:
Can you think of a different way to replot the data so that the graphed data points will lie approximately on a straight line?

Hint: The theory predicts that 1/o + 1/i = 1/f. Thus, if you construct (from your measured o's and i's) new variables x and y defined by x = 1/o and y = 1/i, the equation 1/o+ 1/i = 1/f can be rewritten y = -1 x + 1/f. This is the equation of a straight line of slope -1 and y-intercept 1/f. Plotting y on the vertical axis vs. x on the horizontal axis, the data points should lie on a straight line with the predicted slope and y-intercept.

Question:
Do the points on this graph appear to lie on a straight line?

If you like, take additional data and add these points to fill in your graph more completely.

Draw the best straight line through your data points using a straight edge. Determine the slope and y-intercept of this line and record these on the data sheet.

Question:
Does the slope agree with the prediction? You might answer this question by checking if a line that does have the predicted slope can be drawn equally well through the data points.
Question:
Obtain an estimate of the focal length from your data. Remember that the y-intercept of your line is predicted to be 1/f.
Question:
Predict the image distance when the object distance gets very large, i.e., becomes infinite.
Question:
Compare this prediction with the results you already obtained while using the TV as the object. Was the object distance large enough to be considered infinite? That is, could you see a significant difference between the focal length as obtained from the inverse of the y-intercept and the image distances measured with the TV?
Question:
Can you think of a way to view the image for an object that is very, very far away? Hint: Try imaging a sunlit tree or building through a picture window, the moon on a dark night, or the sun. (Be careful, the sun's image will burn a paper screen---or your flesh, so use a brick or a concrete pavement for your screen. And, of course, under no circumstances should you look directly at the sun especially through a lens.) Try any of these situations (or one of your own), and make an accurate measurement of the image distance. Then compare your results with your previous measurements.

## Comprehension Questions

1. Make a scaled ray diagram for one of the measurements you have made. Show your scale on the diagram, and label the distances involved.
2. The image magnification M is defined as the ratio of the size of the image to the size of the object (and taken as negative sign if the image is upside-down). In the jargon of optics, upside-down images are said to be inverted. An upright image is said to be erect. M is predicted to be -i/o, where the minus sign simply indicates that if i and o are positive (as in this experiment) the image will be inverted. Use some of your data to demonstrate this relation, comparing actual magnifications from your measured image and object sizes, with the values of -i/o determined from your measurements. Use at least one example for which the magnitude of the magnification is greater than 1 (enlarged image) and one example for which the magnification is less than 1 (reduced image).
3. Set the distance between the flashlight and the screen to 70 cm. Scan the lens between the two looking for positions where sharp images form. Did you find exactly two positions? For the two lens positions where an image forms record the object and image distances and the image size. What do you notice about the relationship between the object and image distances at these lens positions? What does the theory predict for the relationship? Compute the magnification for each image formed. What relationship exists between the magnifications? What does the theory predict for the product of the magnifications?
4. Suppose a slide projector is placed 5 meters from the projection screen. The picture on the actual slide is 2 cm by 3 cm. If the image on the projection screen is 1 m by 1.5 m, what is the focal length of the slide projector's lens?