EE 471 Lab 2
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EE471 Lab2: Lens Systems and Basic Optical Instruments
Introduction
The goal of this lab is to understand the imaging properties of thin lenses. You will
construct several lens systems, including beam expanders and a microscope.
Equipment Checklist
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Photodetector circuit board and power
supply.
HeNe laser and power supply.
Photodiode and digital multimeter
Lenses (-25, 25, 50, 75, 200mm)
Kellner eyepiece with reticle
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Optical bench equipment (various – ask
for more parts if required)
Halogen desk lamp and diffuser
Plastic ruler
Object and Image screens (in white 35
mm slide holders)
1. Preliminaries
The first thing to do is to learn to set up and properly align an “optical axis” and “optical
rail” for aligning a number of lenses and the iris (small adjustable aperture). There will be a
demonstration of the alignment procedure at the beginning of the lab. The alignment consists of
four parts:
Basic alignment procedure:
 Align the HeNe and screen at opposite ends of the optical bench.
 Set the iris height so that the laser passes through it when it is most closed. Then use the iris
to align the ruler with the base of the iris post. Check that the ruler is aligned to the laser
beam by moving the iris along the ruler (the iris will not block the beam anywhere along the
length of the ruler when everything is aligned properly).
 Set the height of the lens holders.
 Check the alignment of the system with the various lenses you will use.
2. Beam Expander
In this section, you will expand the HeNe beam using two kinds of
beam expanders and verify that the measured beam sizes agree with theory.
 First, measure the Full-Width-Half-Maximum (FWHM) of the HeNe
beam using the photodiode (it is covered with a crude pinhole to increase
spatial resolution). You only need 3 data points when doing the FWHM
measurements. Align the beam so that it hits the photodiode that is
mounted on the translation stage. Measure the maximum voltage, and
the points where the maximum voltage drops by a factor of 2. Use
circuit A (left side of the board, switch to the right) for these
measurements.
EE 471 Lab 2 2
 To expand the beam, use the -25 mm PCV lens and the +200 mm PCX lens in the
configuration shown below. Adjust the positions until the expanded beam seems to be
constant as a function of position. Measure the lens positions and the FWHM beam size of
the expanded beam using the photodiode as done previously.
HeNe beam
-25
mm
Expanded beam
+200 mm
f1
f2
 Next, repeat the measurements (lens positions and beam FWHM) using the +25 mm PCX lens
and the +200 mm PCX lens in the configuration below.
+25
mm
HeNe beam
f1
Expanded beam
f2
+200 mm
The laser and translation stage are not required for the rest of this lab, set them to the
back of your optical bench.
Report: For each case, calculate the ABCD matrix for the lens-gap-lens. Use the ABCD
matrix to find the output ray if the input ray is at a distance of half the FWHM of the
un-expanded HeNe beam (measured in Section 1) and parallel to the axis. Compare
the predicted and measured beam sizes.
3. Imaging with a single lens and the Lensmakers’ Formula
In this section you are going to verify the imaging equation (also known as the Gauss
Lens Equation or the Lensmakers’ Formula) by finding and measuring the image of the object in
the lamp.
 Use the 50 mm PCX lens to image the object on the screen. Set the lens about 100mm in
front of the object and then move the screen to find the image.
 Place the iris next to the lens on the screen side. Examine the effect of closing the iris down
on the image. Make sure the iris is at the same height as the lens.
 Place the lens at 5 different positions from the object starting at a distance of 60mm and going
in steps of 20mm. Record the position of the image and its size on the screen at each different
position of the lens.
EE 471 Lab 2 3
Report: Include a sketch of the set-up labeled with the measured distances. Build a table with
the following headings:
Position Measured
#
Z1
Measured
Z2
Predicted
Z2
% error
Measured
Image
Predicted
Image
% error
The predicted values are those given by the imaging equation.
4. Imaging with a lens combination and the ABCD matrix
In this section you will use a combination of the 50 mm and the 75 mm PCX lenses to
make an inverted image and non-inverted image.
Inverted Image
 Place the 75 mm lens close to the 50 mm lens on the screen side and find the image with the
screen. Use the iris if it helps position the screen accurately.
 Accurately record all positions and the image size and orientation.
Image
Object
50 mm
75 mm
Non-inverted Image
 Find the image plane of the 50 mm lens and place the 75 mm lens on the other side (screen
side) and again find the image with the screen. You should be able to find an upright image of
the object.
Intermediate
Image
Object
Image
50 mm
75 mm
Report: Include a table of your measurements. In each case, calculate the ABCD matrix for
the lens-gap-lens-gap from the measured positions and known focal lengths of the
lenses and predict the image position and size. Compare to the measured values.
EE 471 Lab 2 4
5. Simple Compound Microscope
The figure below illustrates the simplest form of the compound microscope which is a
two-lens system designed to enlarge nearby objects. The lens near the object to be enlarged
(small arrow on the right, size h0) is called the objective lens and it forms a real, inverted and
magnified intermediate image (large down arrow) of the object when the object is just outside
the focal point of the lens. A second lens called the eyepiece, or ocular, has a short focal length
and allows the eye to focus on the nearby intermediate image making it appear large.
h0
h0
hI
Compound Microscope
The ratio of the angle, a, of the intermediate image as seen by the eye through the eyepiece to
the angle, u, of the object seen by the unaided eye is called the magnification:
M = a / u
This is illustrated below. (A similar definition applies to telescopes.)
dI = fe
a
hI , magnified image of the object.
u
object
Using the small angle approximation, u is the height of the object divided by the distance from
the eye to the object, u = ho / do. When the intermediate image is at the focal point of the
eyepiece, the eye perceives it to be infinitely far away and is relaxed when viewing it (for normal
vision). The angle of the intermediate image seen by the eye is the height of the image, h I,
divided by the distance to the image which is approximately the focal length, fe. Therefore, a =
hI / dI = hI / fe . The overall magnification of the microscope, M, is then
ho
EE 471 Lab 2
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M = a / u = (hI / fe)/(h0 / d0) = (hI / h0)*(d0 / fe).
The latter expression appears as a product of two magnifications,
M = MTo * MAe ,
where MTo = (hI/h0) is the ratio of the image size to the object size, the “transverse linear
magnification of the objective”, which is (from the diagram above – similar triangles)
MTo = hI / h0 = L / fo ,
and MAe , the angular magnification or “power” of the eyepiece,
MAe = do / fe.
Often this power is written on the side of microscope (or telescope) eyepieces where d0 is taken
to be 25.4 cm (10 inches), the standard closest viewing distance for normal eyes.
Procedure:
 Build a microscope system as follows.
o Orient your ruler so that it is front-to-back on your optical bench. This is so that you can
look into your microscope more easily over the edge of the bench.
o Set up the 50mm PCX as the objective lens.
o Set L to be approximately 160mm, and place the screen in the plane where the
intermediate image should be. For L to be 160mm, the distance from the objective lens
to the intermediate image will be approximately 210mm (L+ fo).
o Use the transparent sheet with 1 mm lines as the object and illuminate it from behind with
the halogen lamp. The lamp is very hot so keep it at a safe distance from any paper or
plastic material. Move the object until the intermediate image is in focus on your screen.
o Then remove the screen and replace it with the eyepiece. Adjust the position of the
eyepiece slightly to correct the focus if necessary. Your image will most likely be quite
fuzzy and look “washed out”.
o Insert the iris into your microscope system between the eyepiece and the objective lens
(place it next to the objective lens on the eyepiece side). Change the diameter of the
opening and you should observe two effects (or more) as you focus your microscope with
different iris openings.
 Take measurements so that you may calculate the magnification of this system. (M = a / u)
This is done by using the reticle (scale) in the eyepiece with the known size of the object.
 The next step is to re-design the microscope to a magnification of approximately 20.
Calculate the required separation of the lenses from the formulas given above to achieve this.
Measure all distances as accurately as possible and then the magnification.
6. Report:
EE 471 Lab 2
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With a diagram, describe the microscopes you assembled and their properties. Describe
the object, its size and distance, the lenses used. For the dimensions you used, compare the
theoretical magnifications to the measured magnifications. Discuss the possible causes of any
differences that you obtain.
Many standard microscopes use L = 160 mm so that the transverse linear magnification
of an objective can be written as a power such as 5X, 10X, 40X, etc., when used in different
microscopes. Then the overall microscope magnification can be written as M = (power of the
objective) X (power of the eyepiece) and these are written on the side of these optical elements.
For a 5X objective, the focal length is 32 mm. The power of your eyepiece is 10X. What would
the power of the objective lens you used be if it were packaged as an objective lens for such a
standard microscope?
Give an explanation for the two noticeable effects when the iris is used.
Old Zeiss Microscope and Eyeball