## Kylie having a rough day. I am a student

Kylie Litaker

Egloff

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IB Math

December
2017

Effects of Focal Points in
Photography

Research
Question:

How does the use of focal points
impact the focus on a object in photography?

Introduction:

Art is something I enjoy putting
forth effort on throughout my everyday life.
I love art because it de-stresses me and works therapeutically when I am
having a rough day.  I am a student in IB
art, so almost everyday I get to spend time doing something I really
appreciate.  This topic in specific
incorporates one of my favorite art mediums:
photography.

Aim:

My aim is
to prove that focal points help in the formation of creating images with an
object of interest.  I plan on using my
own personal photos to experiment with the use of focusing images.   In this study I hope to learn more on the
math side of how the use of a focal point will impact my own personal
photography.

Photography is the art or practice
of taking and processing photographs.

A focal point is the point at which rays or waves meet after
reflection or refraction, or the point from which diverging rays or waves
appear to proceed.  It is also the center
of interest or activity.  Focal points
are used to portray a photographer’s point of view.  Photographers are the “authors” of their
photos because they have the option of what or what not they want the main
focus of an image to be.

The reason a focal point is
important is that when you look at an image your eye will generally need a ‘resting
place’ or something of interest to really hold it.        Throughout the duration of this investigation, I plan on
contrasting the difference on how greatly distance and the angles in
photographs being taken are affected.  I
will be testing the effects of focal points on photography with a close up
focus range held at 2.5 centimeters and a further focus range 5 centimeters in
distance.

After conducting the photo
taking,  I am going to use focal length
on the given data to examine what distance from an object will clarify an
image.   The Unit Circle will provide me
with angles that I will then use to position the camera to those angles
(0-180).  Angles are a very important
element in photography.  Different angles
portray different perspectives of an image.  2.5 centimeters and 5 centimeters are the two
varying distances I chose to experiment with considering the high resolution
photos (2.5 cm distance) and further-range (5 cm distance) photos will then be
compared in two different tables displaying the collected data.

Experimentation:

I will start the collection of my
data by incorporating the unit circle angles into photo taking.   I plan on doing this by placing my camera on
a tripod and measuring out the specific angles between 0-180 degrees using a
protractor.  I will tilt the camera
accordingly to the angles being experimented with.  Then, I will compare how clear the photos are
from two different varying distances such as 2.5 centimeters and 5 cm using a
centimeter ruler.  After I finish
collecting the data, I will insert the two trials into two different tables to
compare the angle to distance ratio that impact photo taking.  Once the data collection is complete, I will
then perform a T-test to determine if there is a significant statistical difference
in the resolution of the photos based off of the different distances from the
object in the photo.  I then can state my
null hypothesis, alternate hypothesis, and a conclusion to this Mathematical
Exploration .

Table
One

Distance from Object 2.5 cm Away

Angle
Degree

Focus?
(y/n)

0

No

15

No

30

Yes

45

No

60

Yes

75

No

90

Yes

105

No

120

No

135

Yes

150

Yes

165

No

180

Yes

This chart displays the first
collection of data being 2.5 centimeters in distance away from the focal point
in the photo using the unit circle angles from 0 to 180 degrees.  In table one,
there are six angles out of thirteen angles in which the object was
clarified in the image.  However, seven
out of the thirteen angles did not have a high enough resolution or distance to
clarify the image.  Based off of the data
collected in Table One, there is more of a likelihood that the images will be
unclarified at a distance of 2.5 centimeters.

Focused
Ratio- 6:13   Percentage= 46.153846

Unfocused Ratio- 7:13
Percentage=  53.846153

Table
Two

Distance from Object 5 cm

Angle
Degree

Focus?
(y/n)

0

No

15

Yes

30

Yes

45

No

60

Yes

75

Yes

90

Yes

105

Yes

120

Yes

135

Yes

150

Yes

165

Yes

180

No

Based off of the data shown above in
Table Two, there is a higher ratio of focused images to unfocused images.  There is a total of ten out of thirteen
angles that provide enough resolution to clarify an image.  This leaves the other three angles
unclarified in the photos.

Focused
Images- 10:13  Percentage= 76.923077

Unfocused
Image- 3:13  Percentage= 23.076923

Above
is an image showing the distance                                Above
is an image of the photo taken

2.5
cm away at a 75 degree angle.                                          5
cm away at a 75 degree angle.

–
Unfocused                                                                  – Focused

T-test

Null
Hypothesis:  There will be no
statistically significant difference between the data from table one and table
two.

Alternative
Hypothesis:  There will be a
statistically significant difference between the data from table one and table
two.

P
value and statistical significance:

The two-tailed P value equals 0.0494

By conventional criteria, this difference is
considered to be statistically significant.

Confidence
interval:

The mean of Group One (Distance from 2.5 cm)
minus Group Two (Distance from 5 cm)
equals -0.3

8

95% confidence interval of this difference:
From -0.77 to -0.00

Intermediate
values used in calculations:

t = 2.0702

df = 24

standard error of difference = 0.186

After
completing the t-test, I was able to see that there was a statistically
significant difference between the two tables of data.  This therefore means that the null hypothesis
was rejected.

Reflection:

Throughout this investigation, not
only have I tested the effects of focal points in photography using distance,
but I have also found no statistical difference mathematically between the two
tables of data collected.  I think I
could have proceeded with things differently by collecting more data from different
distances to see more of a result in the clarification in images.  This would provide for me a larger pool of
data to test the effects of focal points on.

Conclusion:

From the
data collected, I was able to predict that there is indeed no significant
statistical difference in the two different tables showing the different
distances used to produce either a focused or unfocused image from either 2.5
cm away or 5 cm away.  Along with
collecting data, I also completed a T-test which showed me that the null
hypothesis was rejected.  The effect of
focal points on photography makes a difference to the naked eye, however,
statistically not so much.  As you
observed the example of the photography of the apple at 75 degrees from 2.5 cm
and 5 cm, you can see a visual difference between the images;  one is unfocused (2.5 cm distance), while the
other is focused (5 cm distance).
Distance makes a key difference within achieving the focus on an
image.  For example, in table one,  there is a higher number of unclarified
images to clarified images which indicates that the distance at 2.5 cm away
from the object (apple)  is more likely
to produce unfocused images no matter the angle.  Although table one produces more unfocused
images, table two shows there is a higher number gathered in the focused images
over the unfocused images.  From this I
can predict that distance does indeed play a role in the resolution creating a
clear and precise image within a focal point.

Sources:

Waterman, Jill. “The Importance of Focal Points in
Photographic Composition.” B Explora, B Photo Video, 31 Mar. 2016, www.bhphotovideo.com/explora/photography/tips-and-solutions/importance-focal-points-photographic-composition.

Waidler, Samantha. “Simple techniques for shooting close-up
photos.” PCWorld, TechHive, 26 Dec. 2012, www.pcworld.com/article/2012265/simple-techniques-for-shooting-close-up-photos.html.

Photography and Math, www.mrmartinweb.com/photomath.html.

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