Visual Photometry
Lenses and Telescopes – Part 1
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LENSES AND TELESCOPES – PART 1
Purpose: In this lab, we will measure two critical properties of lenses (focal length and diameter) and learn how
to make a simple refracting telescope.
In part 2 of this lab, on page , we will briefly discuss field of view (how much you can see through a
telescope/lens system), magnification, and telescope aberrations. We will also learn what role lens diameter and
focal length have in telescopes and what you should pay attention to when purchasing a telescope by studying
the equipment we use with our telescopes on the Math roof.
Introduction
Most of the basic characteristics of a lens can be determined by two properties: the focal length and diameter.
We will concentrate on relating lens and lens system characteristics to these two properties.
You should have the following equipment:
4
Convex lenses, labeled A, B, C, and D
1
Optical bench (the meter stick)
2
Optical lens holders
1
Piece of cardboard with ruler markings on the bottom
1
Flexible ruler
1
Adjustable diaphragm
In the front of the room, you should see a few lights in a triangular constellation.
Measuring the fundamental properties of lenses
Diameter
Compare the diameters of the lenses by eye by lining them all up front-to-back to compare sizes. Just below
table 1, record any observations you may have. Afterwards, use the flexible ruler to measure the diameters of
the four lenses in your equipment box. Record the diameters for each lens in Table 1, page 5.
Focal length
To measure focal length, you must make an image of a distant light source onto the cardboard screen supplied.
The “distant” part is required so that incoming light rays are nearly parallel when they hit the lens. If light
beams are not parallel, our measured lengths will be slightly, but systematically, different from the true focal
length.
Once you have created a well-focused image of the light “constellation” in the front of the room, the distance
from the lens to the focused image is the lens’s focal length. When focused, your image will resemble the light
sources, but perhaps it will be oriented differently (i.e. flipped horizontally, rotated 90º, or something like that).
View the cardboard from behind the cardboard (i.e. look on the “back” side of the cardboard – not on the side
where the light is hitting).
To form an image of the light source(s), set up your optical bench as described below in the step-by-step
procedure below. We will detect the image – which is also what your eye’s retina does – by placing cardboard
behind the lens. (See “vocabulary note” below.) When the image is clearest and most in focus on the cardboard,
record the distance from the image to the lens in Table 1.
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Lenses and Telescopes – Part 1
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Step-by-step procedure
1) Put the optical bench on your table so that the end where the ruler reads zero centimeters is nearest the back
of the room. The other end should point at the lights on the table in the front of the room.
2) Put the white cardboard into a holder on the optical bench and slide it to position 0 cm.
3) Put lens D into another holder on the optical bench near position 40 cm.
4) Line up the lens and cardboard so that the three-light constellation at the front of the room shines through
the lens onto the cardboard.
5) Slide the lens towards 0 cm until the three-light constellation focuses on the cardboard.
6) Read the distance between the cardboard and the lens from the ruler. That is the focal length; it is the
distance between the lens and the cardboard.
7) Repeat these steps for lenses C, B and A.
Vocabulary note: throughout the rest of this lab, placing something “in front” of a lens means place it near
the lens, but on the side closer to the target (e.g. the light source[s]), and “behind” the lens means on the side of
the lens opposite where the light source is, closer to you.
After focusing the image, place the diaphragm behind the lens, but very close to (but not touching!) the lens.
Slowly close the diaphragm. By closing the diaphragm, we are creating a lens with a smaller diameter. Observe
what happens to the focal length of the lens. Then repeat all of these steps for each of the four lenses.
Answer questions 2 & 3 before proceeding, on page 4.
f-ratio
Now compute the f-ratio (also known as the “f-number” or “f/#”) for each lens. The f-ratio is the focal length
divided by the lens diameter. A lens that has an f-ratio of 10 is an “f/10 lens.” An f/5 lens has an f-ratio of 5, etc.
Complete table 1 and answer question 6.
f-ratio = focal length ÷ diameter
Objective Lens and Image Size
Important note: For this one section of the lab, you will want to get as far from the light sources as you
reasonably can. This will make your images larger and easier to see.
Now that we have measured the fundamental lens properties, we are ready to start building telescopes. The first
lens in a telescope is used to create an actual image of the target (i.e. the 3-light sources). In telescopes made
from lenses, called refractor telescopes, the first lens is called “the objective lens.” Set up the telescope as
above, with the D-lens focusing an image onto the cardboard. Leave enough room so that there is 50 cm behind
the cardboard for future lenses.
Now, measure the image size on the cardboard by referring to two of the lights in the constellation that you can
measure most easily and accurately. Which pair you pick doesn’t matter, as long as you always use the same
pair. Do this for all 4 lenses and record the values in Table 2. Also compute the focal length divided by the
image size for each lens and fill in the 2nd row of table 2.
Eyepiece Lens and the Real Image
Focus the lights on the cardboard using the D-lens. You may have noticed that the lights were very close to each
other. If the constellations were words, you might use a magnifying glass to enlarge them. Feel free to try this
with the magnifying glasses provided up front (if any). If there are none available, use one of your other lenses
as a magnifying glass. (Magnifying glasses are nearly identical to the lenses you are using in this lab.)
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Lenses and Telescopes – Part 1
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Now you will use this same setup to build a simple refracting telescope. Use the A-lens as your “magnifying
glass” and place it behind the cardboard (and the D-lens). Adjust the distance between the cardboard and the Alens until the image is in focus when looking through the A-lens at the D-lens and the lights. When this is done,
remove the cardboard and look through your telescope! The A-lens is acting as the telescope’s eyepiece.
About the eyepiece: You are taking a focused image (on the cardboard, when it was there) and viewing it
through a second lens. This second lens takes the “focused” light and makes it into parallel light beams, to make
eye-viewing possible and comfortable for your eye. Hence we call the A-lens the eyepiece lens. Without the
eyepiece, you would need to project the image onto a cardboard screen, or look through the objective (D-lens)
and strain your eye to see the target.
Answer question 8 now.
Light-Gathering Power (LGP)
To measure how much light is gathered by a telescope, we will be measuring the brightness of our target. The
brighter the target appears, the more light was gathered by the telescope. We will be checking to see how the
LGP varies as we change the diameter of the objective lens and also how LGP varies as we change the diameter
of the eyepiece lens.
We will simulate varying the diameter of a lens by placing the adjustable diaphragm in front of the lens. Put the
diaphragm as close to the lens as possible, but leave a little space between them so that the diaphragm doesn’t
touch (and scratch) the lens. As before, opening and closing the diaphragm effectively changes the diameter of
the lens.
Using the telescope created as above, open the diaphragm all the way (so that all of the lens is in use) and place
it directly in front of the objective lens. Then point your telescope towards the targets. (Remove the cardboard,
if you haven’t done so already.)
Important note: When viewing from the back of the telescope (behind the eyepiece lens), it is important to
place your eyes at a place called the eye relief point. This place is where you will see the image of the
objective lens filling in the entire eyepiece lens. In other words, you should not see any unfocused background
stuff around the objective lens. Make sure you do this from now on!
Watch the BRIGHTNESS of the light targets as you close down the diaphragm. Answer question 9A now. Then
relocate the diaphragm so that it is nearly touching (and in front of) the eyepiece lens and answer question 9B.
Something to think about: which lens’ diameter controls the LGP of the system?
Answer any other questions if time permits. All questions and tables should be submitted (individually) at the
next class.
Answer all of the following questions on your OWN sheet of paper – there is not enough room here.
Questions
1. This question has been deleted. Skip to #2.
Important note for the questions: For all of the questions, make sure you specifically refer to your data
when answering the questions. (For example: in table 1, we saw lens-5 did this while lens-10 did that. This
means…)
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Lenses and Telescopes – Part 1
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2. [3 pts – In class] How does the orientation of the image of the lights compare to the actual layout of the
lights? Be specific. For example, if you say flipped, specify which way (e.g. left/right are switched, if you
say rotated, say how much (e.g. 90º).
3. [3 pts – In class] A) Does the focal length depend upon the lens diameter? (In other words, did the focal
length change as you closed the diaphragm? B) How does the focal length depend on the curvature of the
lens? As the lens gets more curved/round, the focal length increases or decreases – which is it? (Curvature
can be measured by how thick the lens is in the middle compared to the edge).
4. [2 pts – Homework, in class time permitting] What happens to the f-ratio if the focal length is fixed but the
lens is made larger?
5. [2 pts – Homework, in class time permitting] A) Which objective lens gives the largest image? B) Which
objective lens gives the smallest image? C) Summarize how the image scale depends upon focal length.
6. [2 pts – In class] A) How does the f-ratio compare to a lens’ roundedness? [Roundedness here does not refer
to the circular shape of the lens – look at the thickness!] B) Which lens would you expect to look rounder, if
the diameters were the same: an f/3 lens or an f/4 lens? Justify your answer. [Recall: f/3 means the f-ratio is
3.]
7. [1 pt – Homework, in class time permitting] A) Describe in words the image size depend on the focal
length? B) What happens to the ratio of these two quantities as the focal length increases? [consult row 2 in
table 2]
8. [2 pts – In class] A) How far apart are the two lenses from each other? B) In theory, this distance should be
related to the fundamental properties of the two lenses you use. What is this relationship?
9. [2 pts – In class] A) What happens to the overall brightness of the image of the board as the diaphragm
opens and closes in front of the objective lens? Don't worry about contrast or clarity or sharpness, just
brightness. B) Same question, except when the diaphragm is in front of the eyepiece lens.
10. [3 pts – Homework, in class time permitting] A) What are two purposes for the objective lens in a
telescope? B) What is the purpose of the eyepiece lens in a telescope?
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Lenses and Telescopes – Part 1
Table 1 [1.5 pts]
Lens
A
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B
C
D
B
C
D
Diameter
Focal Length
f-Ratio
[1 pt] Observations about lens diameters:
Table 2 [2 pts]
Lens
A
Image size
FL / img size
[½ pt] BEFORE LEAVING, GET THE INSTRUCTOR’S OR TA’S SIGNATURE ON THIS PAGE. Also
make sure you have answered all of the “In-class” questions.
Any feedback you would like to provide is appreciated.
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