“Refraction”
Adam Capriola
Experiment Performed: 4/20/10
Report Due and Handed in: 4/21/10
Name of Partner: Ben York
Purpose
To develop an understanding of how light is refracted, to apply the concept of refraction to the
study of how thin lenses form images, to learn to draw ray diagrams to assist in the predicting the
locations of images formed by spherical thin lenses, and to determine the focal length of a
converging lens using three different methods.
Hypothesis
When light hits the convex lens, it will refract and converge at a point in front of lens that will be
construed from the rays diverged behind the lens. The distance between this point of
convergence and the lens is the focal length, which should be similar in value to an indirect
measurement of the focal length of the converging lens by varying the distance between the lens
and an object. Using the distance between the lens and object and the lens and projected image,
the focal length will be able to be determined using the thin lens equation 1/p + 1/q = 1/f. As the
object is moved further past the curvature, the image will become smaller. The closer the object
is moved to the lens between the curvature and focal length, the image will become larger.
While the object is beyond the focal length, the image will be real and inverted. Once the object
is placed between the focal length and lens, the image will become virtual and upright. Finally,
the focal length interpreted using the conjugate method should also be similar to the previous
focal length measurements.
Labeled Diagrams
See attached sheet.
Data
Part 1:
Position of object Real or virtual
Upright or
Image smaller or
Location of
image
inverted image
larger than object image
1. Beyond C
Real
Inverted
Smaller
Between F and C
2. At C
Real
Inverted
Normal
At C
3. Between C
Real
Inverted
Larger
Beyond C
No image
No image
No image
No image
Upright
Larger
Between F and C
and F
4. At F
5. Between F and Virtual
the lens
Part 2A:
f = 7.70 cm
Part 2B:
p (cm)
q (cm)
f (cm)
20.0
11.8
7.42
17.0
13.2
7.43
15.4
14.4
7.44
13.0
17.3
7.42
11.5
19.7
7.26
faverage = 7.40 cm
Part 2C:
First conjugate position (cm)
Second conjugate position (cm)
43.3
10.2
f = 7.41 cm
Questions
1. What is the measured value of the focal length and how does it compare with the given value
of focal length for the length for the lens?
The measured focal length is 7.70 cm which is fairly close to the given value of the focal length,
7.50 cm. The percent difference is 2.63%.
2. For each p and q in your data table above, calculate f. Record in your data table.
See data table.
3. Calculate and record the average value of your f’s.
The average value of the focal lengths is 7.40 cm.
4. How does the average focal length compare with the focal length printed on the lens? What is
the percent difference?
The average focal length calculated is slightly less than the focal length printed on the lens. The
percent difference is 1.34%.
5. Calculate the focal length of the lens using f = (D2 – d2) / 4D where D is the distance between
the object light and the image screen and d is the distance between the two conjugate positions.
D = 51.1 cm and d = 33.1 cm, so f = 7.41 cm.
6. How does this value for the focal length compare to the given value of the focal length for the
lens? What is the percent difference?
This value for the focal length is again slightly less than the given focal length of the lens. The
percent difference is 1.21%.
7. How do your focal lengths calculated from Parts 2A, 2B, and 2C compare? What is the
percent difference between f from 2A to 2B? 2A to 2C? 2B and 2C?
The focal lengths from part 2B and 2C are nearly identical, while 2A is a tad larger than each of
them. The percent difference between f from 2A to 2B is 3.97%, from 2A to 2C is 3.84%, and
from 2B and 2C is 0.135%.
Conclusion
During part 1 of the experiment, ray diagrams of thin lenses were constructed for the
following scenarios: an object beyond the curvature, an object at the curvature, an object
between the curvature and focal length, an object at the focal length, and an object between the
focal length and lens itself. The image size, orientation, location, and realness were predicted
and recorded for each scenario. These predictions were used to aid with part 2B of the
experiment.
During the half of the experiment, the focal length of a positive lens was measured in
three different manners. The first of these methods, part 2A, used the application of a direct
measurement to find the focal length. Equipment was set up on the optics bench so that light
shone through a parallel ray lens, slit plate, and 75 mm convex lens onto a ray table. The parallel
ray lens was first adjusted in order to align the light rays in a parallel manner before placing the
75 mm convex lens in front of the ray table. The light rays refracted through the lens and
diverged onto the ray table. The outermost rays were traced on a piece of paper and were
extended to meet at a focal point. The distance between this focal point and the lens was
measured as 7.70 cm and recorded as the focal length. This was 2.63% difference from the given
value of 7.50 cm as the focal length of the lens. This error can be attributed in part to difficulty
keeping the tracing paper in place. It undoubtedly shifted some during tracing of the light rays.
It was also difficult decipher the exact distance from that drawn point to the lens, as they were
not on the same plane; the ray table was elevated and at an angle in relation to the lens. These
attributions are most likely what led to that slight error.
During part 2B, the thin lens equation, 1/p + 1/q = 1/f, was used to measure the focal
length. The crossed arrow target was placed at five positions beyond the measured focal length
from of the lens part 2A. The distance from the lens to object (crossed arrow target) and from
the lens to focused image were recorded for each instance. As the object was moved further
away from the lens, the image became smaller, and as it was moved closer to the lens, the image
became larger. The image was real and inverted in all cases. The average focal length from
these recordings was calculated to be 7.40 cm, which was 1.34% different than the given focal
length of the lens. The minor error could be attributed to difficulty locating the exact position
where the image was truly focused; there was not definitive way to tell if the image was focused
or not. There was likely some error in the interpretation of the positioning of the instruments as
well, due to their thickness. Each measurement may have been misread by a couple tenths of a
centimeter.
During part 2C, the conjugate method was used to measure the focal length. The method
called for the crossed arrow target to be placed directly in front of the light source with the
viewing screen at the opposite end of the optics bench, as far away as possible. The 75 mm
convex lens was positioned between the object and viewing screen, adjacent to the crossed arrow
target. The lens was slowly moved towards the viewing screen until a large focused image came
into picture on the viewing screen. This positioning was noted and recorded as the first
conjugate position. The lens was then moved towards the viewing screen until a minute focused
image came into picture. This positioning was noted and recorded as the second conjugate
position. The distance between these two positions was recorded as d and the distance between
the crossed arrow target and viewing screen was recorded as D. These values were subbed into
the equation f = (D2 – d2) / 4D to find the focal length. It was calculated to be 7.41 cm using this
method, which is 1.21% different than the given focal length. Error from this part of the
experiment could again be attributed to possibly not getting the image in perfect focus, which
would through off the positioning. Moreover, it was also difficult to read the exact positioning
of the lens, object, and image as these apparatuses all had a thickness to them. As in part 2B,
there may have been a couple tenths of a centimeter error in each reading. The measured and
calculated focal lengths from all three methods were fairly consistent. The focal lengths from
part 2B and 2C were nearly identical, while 2A was a small amount larger than each of them.
The percent difference between f from 2A to 2B was 3.97%, from 2A to 2C was 3.84%, and
from 2B and 2C was only 0.135%.
Equations
C = 2f
1/p + 1/q = 1/f
f = (D2 – d2) / 4D
Percent Difference = |x1 – x2| / (x1 + x2)/2 x 100%