Part 1-Lenses
For the exercise below, answer all questions in the spaces provided.
Lenses
Lenses have been used for centuries. The oldest lens artifact is more than 3,000 years old and was
probably used as a magnifying glass or to start fires. The first “microscope was just a magnifying glass at
the end of a tube. It could magnify ten diameters (10X). They were used to look at small critters and
were known by the public as “flea glasses.
At the end of the 16th century, two Dutch spectacle makers, Zaccharias Janssen and his son Hans
discovered that when you put two lenses together and looked at an object, its image was magnified.
This discovery eventually gave rise to both the microscope and telescope. In the early 17th century,
Galileo figured out the physics of what was going on and was able to refine this into a sensitive
telescope.
At about the same time, Anton van Leeuwenhoek of Holland, as an apprentice in a store where
magnifying glasses were used to count threads in cloths, figured out more refined ways to grind and
polish lenses that were curved. By this technique, he was able to get magnifications of up to 270 X. As
the father of modern microscopy, he was the first to see and describe what he referred to as “wee
beasties”…..bacteria, pond life, yeasts, etc. He also examined human parts such as blood.
Let’s take a look at the physics and lens optics behind a microscope.
Microscope lenses are biconvex. You may remember from the lens section of your 10th grade course that
a biconvex lens looks like the lens pictured below and the light traveling through the lens refract and are
drawn as rays.
Last year, while learning about lenses, you used the diagram below:
Biconvex lenses- Optical Engineering
1. As you did last year, continue rays I1, I2, and I3 through the lens. Remember that I2 and
I3 are striking a curved surface and in this case they will both strike at the same angle
whereas I1 is striking perpendicular to the surface. Label the focal point (F) and the focal
length (f).
2. Okay, now let’s try working with the same sort of situation but let’s look at 3 rays
coming in from the top of an object…in this case an arrow:
3. Continue the 3 rays through the lens. Remember that a ray passing through the focal
point will pass through the lens parallel to the principal axis. Draw the image of the
arrow on the opposite side of the lens.
4. Would the image produced be upright or inverted?
5. Note that the rays are recombining after refraction. Is this a real or virtual image?
Could it be projected onto a screen?
6. The lens above has two symmetrical faces. How would this situation change if one of
the faces was thicker than the other?
7. In the space below, explain why changing the material in a lens would change its focal
length.
8. If you were confined to one material, how could you change the focal length of a lens?
Go to the following site and do the tutorial:
https://phet.colorado.edu/sims/html/geometric-optics/latest/geometric-optics_en.html
9. As the curvature of a lens decreases (by increasing the radius of the curvature on the
simulator), describe what happens to its focal length and magnification?
10. Predict what will happen to the focal length and magnification as you increase the
curvature. Try increasing the curvature to test your prediction.
Biconvex lenses-varying the position of the object
Using the link above, and doing the next tutorial, you can see the specific effects of object distance on
the image distance.
11. What is the ideal placement of an object when you want maximum magnification?
12. Materials seen under a microscope are not all the same height. How do you think a
commercially made microscope helps you accomplish correct placement?
13. Place the object on F. Imagine that you could place a lens so that the projected image of
the Penguin (you can change the object 😉) passed through F of your new lens on the
way to your eye. What do you think would happen to the size of the image?
14. Using your answer to 13 above, explain why it is important that the image through the
biconvex lens is “real”.
15. Imagine that you are projecting an image through a biconvex lens and its magnification
is 40X. You then pass this image through another lens with a magnifying ability of 10X.
What will your total magnification be?
Biconvex Lenses- objects inside of F
Let’s take a look at a magnifying glass to show a biconvex lens. Before we do this, let’s go back to a ray
diagram:
16. As you did in step 2, draw 2 rays, one parallel to the principal axis and one that goes
through the center point. Note, since the object is within F, there is no way to draw the
third ray, through F.
1. Where will the rays intersect?
2. Can this image be projected?
3. Is it real or virtual? Explain your answer.
Ok, let’s think about using a magnifying glass in two ways. First, imagine placing the magnifying glass
close to the fingers of your left hand and holding the glass with your right. Look through the glass at
your finger. Now, imagine placing the glass close to your eye. Bring the fingers of your left hand close to
the lens.
17. In which case did you get a clearer view.
18. Was the image inverted or upright? Do you think it is real or virtual?
To simulate this, go to the diagram on the following site. This is a diagram of how a biconvex lens
operates. Please note, the lens in the diagram has an extremely long focal length, thus the object and
the eye are between the lens and the focal point, F.
Without manipulating the diagram, answer the following questions:
19. Do the refracted rays intersect?
20. Will this form a real or virtual image?
Now, click on the magnifying lens and move it further from the eye and closer to the eye. Observe the
refracted rays in each case.
21. Use the observations from the simulation to explain your answer to question 20,
above.