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### Transcript of © UNT in partnership with TEA - AAVTC: Commercial Photography Practicum – Math in Photography...

© UNT in partnership with TEA - AAVTC: Commercial Photography Practicum – Math in Photography

Math in Photography

© UNT in partnership with TEA - AAVTC: Commercial Photography Practicum – Math in Photography

Math in Photography

● Math abounds in photography in ways that make it seem easy. o Without thinking, a photographer will think in terms

of complex mathematical equations as they adjust their aperture, ISO, and shutter speed.

● An important, but lesser known mathematical relationship in photography is with focal lengths.

© UNT in partnership with TEA - AAVTC: Commercial Photography Practicum – Math in Photography

What Focal Length Isn’t

● The last time we spoke about focal length in-depth was when we discussed lenses.

● Many people just associate focal length as being how “zoomed in” a particular lens is.

● While it is true that the higher the “millimeters” of a lens, the more “telephoto” the lens is considered, the actual definition of focal length measures something else.

© UNT in partnership with TEA - AAVTC: Commercial Photography Practicum – Math in Photography

What is focal length?

● Focal length is the distance in millimeters from the optical center of a lens to the sensor at the back of the camera.

Photo from the public domain.

© UNT in partnership with TEA - AAVTC: Commercial Photography Practicum – Math in Photography

35mm Equivalent

● You may have come across the term "35mm equivalent" when looking at focal length before.

● This term is based upon old film cameras that used 35mm film.

● The term exists to describe the field of view with a lens through cameras that have different sensor sizes.

© UNT in partnership with TEA - AAVTC: Commercial Photography Practicum – Math in Photography

Example

● It used to be that no matter what camera you put it on, a 28mm lens would give you the same field of view.

● However, with the advent of digital cameras, there is no universal relationship between the focal length of a lens and the angle of view that is received.

● Since the size of a camera’s sensor determines the angle of view, a 28mm lens on a film camera would not produce the same image as a 28mm lens on a small digital camera.

© UNT in partnership with TEA - AAVTC: Commercial Photography Practicum – Math in Photography

Cameras with Different Sensor Sizes

The camera on the right has full frame sensor, while the camera on the left has a cropped sensor.

Photo from the public domain.

© UNT in partnership with TEA - AAVTC: Commercial Photography Practicum – Math in Photography

Different Sensor Sizes

● Sensors come in all different shapes and sizes. ● The size and shape of a camera’s sensor determines

the “aspect ratio” of the photos it produces. ● For example, most medium or large format cameras

have a square sensor and produce images with a square aspect ratio because they have a square shaped sensor.

© UNT in partnership with TEA - AAVTC: Commercial Photography Practicum – Math in Photography

Cropped vs. Full Frame

● Most modern day camera sensors fall into two categories: o Full Frame Cameraso Cropped Sensor Cameras

© UNT in partnership with TEA - AAVTC: Commercial Photography Practicum – Math in Photography

Full Frame Sensor

● Full Frame Sensor – Full frame sensors are the same size and shape as 35mm film. Therefore, a lens with a focal length of 50mm would look the same on both an old film camera and a modern day DSLR with a full frame sensor. Its focal length is 50mm no matter what.

© UNT in partnership with TEA - AAVTC: Commercial Photography Practicum – Math in Photography

Cropped Sensor

● Cropped Sensor – A cropped sensor is a sensor that produces images that are a different shape than a 35mm film. It is almost as though the sensor has been “cropped,” or had a portion of it cut off. For this reason, the field of view is smaller than a full frame camera.

© UNT in partnership with TEA - AAVTC: Commercial Photography Practicum – Math in Photography

Field of View

In the image on the right, you can see that the red sensor sees a larger portion of the image than the blue sensor, even though they both have the same focal length.

Photo from the public domain.

© UNT in partnership with TEA - AAVTC: Commercial Photography Practicum – Math in Photography

Field of ViewThe red rectangle is a full frame camera, which has a larger sensor and therefore sees “more” of the image than the blue, cropped sensor camera. It has a wider “field of view.”

Photo from the public domain.

© UNT in partnership with TEA - AAVTC: Commercial Photography Practicum – Math in Photography

● Most lens sizes are named according to what they are on a full frame camera.

● For example, a 50mm lens would have a focal length of 50mm on a full frame camera, but not on a cropped sensor camera.

● Keep in mind what type of sensor you have when purchasing a lens so you know what the true focal length will be.

© UNT in partnership with TEA - AAVTC: Commercial Photography Practicum – Math in Photography

Crop Factor

● “Crop Factor” measures how far a cropped sensor is from a full frame sensor.

● Most cropped sensors have a crop factor of either 1.6 or 1.5.

● Mirrorless cameras have a crop factor of 2. o This means that a 40mm lens would actually have a

focal length of 80mm on a mirrorless camera.

© UNT in partnership with TEA - AAVTC: Commercial Photography Practicum – Math in Photography

Other Ways Photography Deals with Math

● Equivalent focal lengths are just one of the many ways that photography deals with math.

● Many of the other ways are like second nature to seasoned photographers, such as yourselves. o A photographer will adjust aperture, ISO, and shutter speed while

keeping in mind the inverse relationship that exists between them and light.

o The seasoned photographer will also keep in mind their depth of field and how their aperture, focal length, and distance from subject affect the photograph.

© UNT in partnership with TEA - AAVTC: Commercial Photography Practicum – Math in Photography

Review

● Focal length is often different, depending on the size of your sensor.

● Sensors that are the size and shape of 35mm film are called “full frame” sensors.

● Sensors that are smaller than 35mm film are called “cropped” sensors.

● Different sensors have different “crop factors.”