Lab 11
Lenses, Imaging and Intensity
4/14/11
Andrew Do
Ashley Schreckengast
Courtney Stewart
Daniel Trujillo
Aim:
For unit 11 lab we will be looking at lenses. We will look at magnification with diverging and
converging lenses and the position and size of images produced by these lenses. We will use
the lens equation to find the position of our images and the magnification equation to find the
degree of magnification of our image. Then we will test the difference in the intensity of
radiation with regards to moving towards and away from a set source and with light bulbs of
different wattage.
Procedure:
Distances used in calculations that utilize the thin-lens equation or the magnification equation
are defined as positive or negative based on a certain set of rules. In simple terms, if the
absolute value of the magnification is greater than 1 (ǀmǀ > 1), the image is bigger. If the
absolute value of the magnification is less than 1 (ǀmǀ < 1), the image is smaller. If the
magnification is greater than 0, m > 0, or positive it is upright. If the image is less than 0, m < 0,
or negative the image is inverted.
In experiment one, the measurement of focal length of a convex lens; we used an
optical bench, light bulb, convex lens, and two different screens to measure the object distance
and image distance in order to calculate the focal length of the utilized convex lens. Then the
object size and image size were measured to determine the magnification of the convex lens.
This was repeated for a second lens.
In experiment two, the combination of two convex lens, we used the previous lenses
with the aforementioned equipment to make a combination of lens. It should be noted that the
focusing characteristics of a combination of lens can be calculated from the thin lens equation
by assuming that the image of the first lens acts as the object for the second, and so forth. The
net magnification is simply the product of the magnifications of each lens, as determined in
experiment one. Using the experiment, you can measure the image distance and size of the
image to determine magnification with the thin-lens equation and compare this to the product
magnification you determine from experiment one.
In experiment three, determination of focal length for a diverging lens, one must go to
lengths to find the focal length of a diverging lens since the image formed by a diverging lens is
virtual. To do so, one must combine the diverging lens with a converging lens to create a real
image and use the thin-lens equation. You will use the set-up for experiment two, but replace
one convex lens with a diverging lens. You then measure all the distances from the figure
below.
Using these measurements and the thin-lens equation we could then determine the focal
length. Then we could measure the image size and calculate the magnification.
In experiment four, variation of intensity with distance, we observed the variation of
intensity with distance by measuring the relative intensity impinging from opposite sides onto a
photometer using the optical bench, photometer, and two bulbs of varying wattage on either
side of the photometer. We would move the bulbs up and down the bench until they appeared
to match in intensity upon the photometer and would record their positions. One bulb was a
constant 100 watts, and the other was varied in wattage. What we should determine is the
truth that the intensity from the source decreases as the inverse square of the distance when
the intensities at the photometer are equal. In this case, the following relationship should hold.
P100
=
Pb
4πR1002
4πRb2
P(100) is the wattage of the 100 watt bulb, P(b) is the wattage of the second bulb, R(100) is the
distance of the 100 watt bulb from the photometer and R(b) is the distance of the second bulb
from the photometer. Using this relationship, we can calculate the position at which the second
bulb should be placed when the intensities of the photometer are equal and can compare this
to what we measured.
Data:
Experiment No. 1: Measurement of Focal Length of a Convex Lens
Thin Convex Lens
Object Distance: 22.5 cm
Image Distance: 16.5 cm
f-1 = d0-1 + di-1
f-1 = 22.5-1 + 16.5-1
Focal Length: 9.5 cm
Object Size: 2.5 cm
Image Size: -1.6 cm
m = - di/do
m = -16.5/22.5
Magnification: -0.73
Thick Convex Lens
Object Distance: 15.5 cm
Image Distance: 7 cm
f-1 = d0-1 + di-1
f-1 = 15.5-1 + 7-1
Focal Length: 4.82 cm
Object Size: 2.5 cm
Image Size: -1.2 cm
m = - di/do
m = -7/15.5
Magnification: -0.45
Experiment No. 2: Combination of Two Convex Lenses (work shown below)
Measured:
Calculated:
Image Distance:
20cm
23.8cm
Magnification:
1.28
0.33
Object  lens 1
Lens 1  lens 2
Lens 2  image
Hi = 3.2 cm
d01 = 6.5 cm
d = 7.5 cm
di2 = 6 cm
1/d02 = 1/f2 – 1/di2
d02 = -16.3 cm
di1 = d – d02
di1 = 7.5 + 16.3 = 23.8 cm
1/f1 = 1/do1 + 1/di2
f1 = 3.12 cm
m = hi/ho = 3.2/2.5 = 1.28
mcalc = m1 * m2 = -0.73 * -0.45 = 0.33
Experiment No. 3: Determination of “f” for a diverging lens(work shown below)
Focal Length: 4.702
Magnification: 0.44
D(o1) = 6.5
D = 18
D (i2) = 17
1/d02 = 1/f2 – 1/di2
d02 =6.5 cm
di1 = d – d02
di1 =11.5 cm
1/f1 = 1/do1 + 1/di2
f1 = 4.7 cm
H(i1) = 2.5
H(i2) = 1.1
m = hi/ho = 1.1/2.5 = 0.44
Experiment No. 4: Variation of Intensity with Distance
Wattage of Bulb
100W
75W
60W
40W
Position
19 cm
16 cm
13 cm
10 cm
P100/(4𝜋*(R100)2) = Pb/(4𝜋*(Rb)2)
Calculated Position
19 cm
16.5 cm
14.7 cm
12 cm
1/Rb = √100/(192 * Pb)
1/R75 = √100/(192 * 75)
R75 = 16.5 cm
1/R60 = √100/(192 * 60)
R60 = 14.7 cm
1/R40 = √100/(192 * 40)
R40 = 12 cm
Conclusion:
In this lab we studied convex and concave lenses. A lens is an optical device with perfect or
approximate axial symmetry which transmits and refracts light, converging or diverging the
beam. We setup two lenses a certain distance apart and shine a light through a paper with a
design on it, which in turn created a shadow on another paper, and the purpose of this
experiment was to find the length in which the shadow became clear, by moving the lenses
closer or farther apart. Overall the experimentation was a success and the uses of concave or
convex lenses made more sense. Although the possibility of human error was minimal, there
was a chance that the bulbs we used were mislabeled and we lacked the proper equipment to
properly test the wattage of the light bulbs, another possibility was an error in the calculation
part of the experiment in which a rounding error or simple algebraic miscalculation had
occurred. Our results that we obtained were anticipated and we accepted as correct.