Kylie Litaker

Egloff

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

cameras already have. The closer-range

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.