Hi, I’m Michele Del Core! I’m 18 years old and photography is one of my biggest passions. Practicing and doing researches about it, I discovered that maths is involved even in taking photos. I’m going to tell you about this relationship between numbers and… a click!

A beautiful “click”! The close relationship between maths and photography Click on the shutter to begin! Click on the shutter to begin!

introduction. Photography is an art or a process through which still or moving pictures are created by recording radiation on a radiation-sensitive object such as electronic sensors and photographic films. There are different types of cameras all of which are used for the same purpose of recoding still and motion pictures which are later on processed to the most appropriate form. A camera, as an image forming device, uses photographic film or a silicon electronic image sensor as a sensing medium to record the intended details. Cameras works thanks to the shutter, that is like a door. When we take a photo, it opens, letting light hit the film or sensor, and closes to stop the light from hitting the film or sensor. The size of the door is called aperture. And the last of time it’s opened is called shutter speed. Certain mathematical figures and descriptive terms are used to define how we can set a camera for having good pictures. This depicts a close relationship between mathematics and photography that we’ll discover in part trough this presentation. But we have to take confidence with some elements of the camera first.

camera FOCAL LENGTH SHUTTER APERTURE

focal length. The focal length can be thought of how long a lens is. Long lenses makes things appear close up. Short lenses make things look further away but give you a wide angle of view. The focal length of a lens is the distance between the optical center of the lens and the points where a clear image is formed. A camera lens is usually composed of several individual lenses and is called a compound lens. The focal length of modern camera lenses and telescopes is usually measured in millimeters. Short focal length lenses gives you a wide view and are called wide angle lenses. Longer focal length lenses have a narrow view and make things appear closer. They are called telephoto lenses. With a Zoom Lens you can change focal length whenever you want.

shutter. The shutter speed is the part of the camera which adjusts the speed of the shutter in an attempt to control the amount of time taken for the sensor to absorb the light when exposed. This speed is expressed in terms of fractions of seconds. Most also have a B (Bulb) setting where the shutter stays open until you release the button. The speed of the shutter is used to control the amount of light striking the imagining medium such that faster shutters reduces the amount of exposed light thus results in more clearer images being formed. The camera shutter is like a door which opens to let light in. The shutter speeds form a geometric sequence. In moving from 1/1000 second towards 1 second each increase in shutter speed increases the time and the amount of light hitting the film by a factor of 2. The common ratio is hence 2. 1/10001/5001/250 1/1251/601/30 and so on… In few words…

aperture. The aperture (f-stop) is a component of the camera which is useful at adjusting the lens opening hence controlling the amount of light that reaches the sensor. The diameter of the opening is determined by the amount of light that is required by the photograph. In other words, the aperture is how big the door is. Larger the diameter, more light can pass through the lens. Cameras can actually change the size of their aperture. The aperture value affects the depth of field, which is important when the scene includes elements placed at different distances from the camera. What are f-stops?f-stops

f-stops.

the importance of two controls. Both aperture and shutter speed, making sure that the sensor receives the right amount of light, affect the image in different ways. By modifying the amount of light that reaches the sensor, the aperture affects the intensity of light, the shutter controls the time during which the sensor is exposed to light. Each of them has different effects on the image. The exposure time affects the image when either the subject or the camera are moving. The aperture affects the image when there are subjects on different planes. If you want to freeze action you can use a fast shutter speed of 1/1000, 1/500 or 1/250 of a second. Conversely, you might want to blur a fast moving subject to give the illusion of movement by using a slow shutter speed. You might also use a slow shutter speed with the camera mounted on a tripod to give a misty, feathery appearance to a waterfall. If you use a narrow aperture to take a photograph of a person's head with a bookcase behind them, both his or her head and the bookcase will be in focus. If you instead use a wide one, his or her head will be in focus but the books in the bookcase will not. I might want the books to be blurred if you are interested in viewers focusing their attention on the person's face rather than the books.

same scene, two shutter speeds: FAST SHUTTER SPEED SLOW SHUTTER SPEED

the depth of field.

same scene, different depth of field: GREAT DEPTH OF FIELD SHALLOW DEPTH OF FIELD

light. Only the right amount of light must hit the camera sensor, of film. This quantity is called exposure and can be properly got in two ways. Relation between Aperture and Focal Length Relation between Aperture and Shutter Speed

relation between aperture and focal length.

relation between aperture and shutter speed. To get a photograph that is not too dark or not too light the photographer uses the aperture and shutter speeds to control the amount of light hitting the film. The photographer determines how much light is needed by using a light meter, suggestions on the box of film, or from experience. Since the mid 1960s most single lens reflex cameras have light meters inside them. The photographer can set the shutter speed and then move the aperture ring until a needle or light indicates the exposure is right. Conversely, the photographer can set the aperture and then move the shutter speeds dial until the needle or light indicates the correct exposure. Modern cameras will also generally have a setting that will automatically set a proper shutter speed and f-stop. Since there are two variables (shutter speed and aperture) that control the amount of light hitting the film, there are several combinations of shutter speeds and f-stops that will give the same exposure. 1/250 - f41/125 - f5.61/60 - f81/30 - f111/15 - f16

As we said, the possibility of modifying both shutter speed and aperture is really important for a photograph because they affect the picture in different ways. Let’s see it practically! same scene, but: 1/320 secf. 1,4 Fast shutter speed and small aperture value Subject motion stops and the depth of field is shallow. 1/5 secf. 11 Slow shutter speed and large aperture value Subject motion blurred and the depth of field is deep.

exposure value.

in conclusion. If you are interested in photography, but you don’t like maths, don't let that stop your interest. You don't need to understand all the maths here to enjoy photography. If you find maths interesting, but you don't care to photograph, enjoy maths. Photography uses a lot of middle school math concepts. Various aspects of the entire preparations and recording of images are dependent on the photographer’s capacity to apply mathematical knowledge on the process to ensure the high quality of a photo but remember: cameras are just tools. The true joy of photography is finding the harmony in the beauty of nature and the people around us!

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