Objectives

• Observe imaging properties of a lens
• Determine a lens focal length using thin lens equation
• Determine magnification and compare to expected

Introduction

The thin lens equation describes the imaging distances of a lens based on its focal length and object position. The linear magnification produced by a lens is defined as the ratio of image/object heights.

Thin lens equation		p - object distance q - image distance f - focal length h - height
Image magnification

The diagram here shows the three principle rays from one point on the object. Two of these rays extend through a focus point and run parallel to the axis on the other side of the lens. The third ray extends un-deviated through the center of the lens.

Prelab

Textbook reference: see section on thin lenses

Consider this.
You write your name in half inch high letters on a card and place the card as the object at a distance from a lens, in millimeters, equal to the first 3 digits of your student number. You then find an image on the other side of the lens at a distance, in millimeters, equal to 10 plus the last 3 digits of you student number. For example. 953001553 would have the card object at 953mm and the image at 563mm.
Answer the following:

• State your student number
• Draw a sketch showing the lens, your name card, the image and object distances.
• On the sketch show the three principle light rays for imaging a point on your name.
• Calculate the focal length of the lens. (be sure to show your work)
• Determine the magnification of your image. Then determine how large, in inches, the letters in the image are.
• What does the minus sign in the magnification say about the image of your name?

Converging Lens

This experiment uses a double convex lens (a magnifying glass) on your desk. Each student works with their own lens (identified on the lens as student 1 and 2). The lens and screen are held in place by magnetic clamps that can be switched on and off.

A converging lens can produce a real image (where the light focuses to an image). Film that is placed at the image plane would be exposed and could be developed into a picture. Real images are also found with concave mirrors and holograms with images projecting out in front.

Experiment a

• Determine the focal length of the lens directly by obtaining the image of a very distant object on a white card and measuring the image distance.
• Write down a value (an uncertainty) of how accurate you feel this focal length was measured.

Experiment b

• Write your name along with a color drawing on a card. Attach the card with masking tape to the front of a light. This back-lit card will form the object. Place the light into position at one end of the board.
• Adjust the lens height so it coincides with your name on the card. Now, position the lens at some distance (30-60cm) from the object (your light with the card)
• Now find the position of a screen (card on a post) for which an image is in sharp focus
• Measure the object and image distances from the lens as well as the object and image sizes.
• Determine how exact you can measure distance and also how exact the screen can be positioned at the image location. Write down these values as uncertainties (a ± value)
• What effect does covering part of the lens have on the image. (Try covering ½, ¼, or ¾ of the lens and see what happens with the image)

Experiment c

• Separate the object card and the screen by as much as bench will allow.
• Start with the lens close to the screen and find the position at which there is a sharp image on the screen. Measure the object and image distances from the lens as well as image and object sizes.
• Now leaving the object card and screen in the same position, find a second (different) position of the lens where there is a sharp image on the screen and measure all positions and sizes.

Experiment d

• With the lens and screen positioned as they should be from the end of experiment c (with the lens close to the object card and a large focused image on the screen) place the small aperture card directly after the lens.
• This should produce a dimmer image on the screen which should still be in focus.
• Move the screen back and forth to find the range where the image is still in focus (this is referred to as the depth of field)
• Record the screen positions where the image just begins to loose focus.
• ​Remove the small aperture card and compare how the depth of field changes.  Comment on the difference between the depth of field with and without the small aperture card

Analysis

• Determine the focal length of the lens from the measurements of experiment b and c.
• Considering all three experiment values for the lens focal length, write a single statement that states an overall focal length and an overall accuracy for this value.
• For all parts of experiments b and c, determine the expected magnification using the object/image distances and compare to the magnification found from the object/image sizes. Write the comparison statements using percent difference.

Converging Lens Simulation

Click here  to open the simulation

Diverging Lens

Overview

A diverging lens will produce a virtual image, no light actually focuses to the image position. This virtual image can not be projected onto a screen and would not expose film since no light is actually at the image position. Virtual images are very common such as the image in a flat mirror.

Computer Simulation

Click here to open diverging lens simulation

Double Concave lens

• On your desk is a double concave lens.
• Try to determine the image position for some object at several nearby distances. (This is not easy to do, you will probably only be able to make a rough estimate of where the image is)
• Draw a sketch in your notebook of the lens showing your view and the apparent image of a nearby object.
• Describe some experiment that could be done to more accurately determine the image position