MATHS IN PHOTOGRAPHY


FOCAL LENGTH

The focal length can be thought of how long a lens is. Long lenses, like a photographer uses at a football game, makes things appear close up. Short lenses make things look further away but give you a wide angle of view. Now, let’s get a little more technical.

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. We measured the focal length of several magnifying glasses which are one piece, or “simple,” lenses. 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. In between are normal lenses which have an angle of view similar to the human eye. 35mm cameras use film that is 35mm wide.

Common wide angle focal lengths for 35mm cameras are 24mm, 28mm, and 35mm.

Common normal focal lengths for 35mm cameras are 50mm and 55mm.

Common telephoto lenses for 35mm cameras are 100mm, 135mm, 200mm, 300mm and 400mm.

Zoom lenses are popular today. A zoom lens has a range of focal lengths. The photographer changes the focal length with a button on the camera or a ring on the lens. Examples of common zoom lenses for 35mm cameras are 28mm to 80mm, 70mm to 210mm and 100mm to 300mm.

CAMERA APERTURE

The aperture is made up of a set of expandable and contractable metal blades in the camera’s lens that form a hole. This hole is responsible for letting light onto the camera’s sensor. Opening that hole up wide lets the most amount of light onto the sensor while closing the hole down lets the least amount of light onto the sensor.

F/Stops are a ratio of two things: the diameter of the aperture in the lens and the focal length of the lens. For instance, if we had a lens at a 135mm focal length, adjusting the aperture to F/3.5 would mean the aperture (hole) is open 38.6mm (135/3.5 = 38.6). A 135mm lens at F/22 would mean that the aperture is open 6.1mm (135/22 = 6.1). Therefore, the higher the F/Stop (aperture value) the smaller the hole, while the lower the F/Stop the wider the hole.

Traditional apertures double or halve the light. As an example, F/2.0 is twice as bright as F/2.8. F/11 is twice as bright as F/16. The following sequence is the standard for aperture values:

F/1.4   F/ 2.0   F/ 2.8   F/ 4   F/ 5.6   F/ 8  F/ 11   F/ 16   F/ 22

As you look at the above F/Stop sequence, think wide –> narrow. An F/1.4 lens is regarded as a very bright or fast lens while an F/22 lens is regarded as a slow lens. 

Note: The aperture is the size of the hole that light passes through to hit the sensor. The shutter speed is the amount of time the aperture stays open.

CHANGING SHUTTER SPEED

Change the shutter speed to adjust how much light is allowed into the camera for a certain length of time. Camera’s shutter speeds are calculated in fractions of seconds, which are usually 1/1000, 1/500, 1/250, 1/60, 1/30, 1/15, 1/8, 1/4, 1/2 and 1.

Calculating the correct shutter speed to use is a matter of understanding geometric sequence. As you increase the speed from 1/1000 toward 1 second, each increase multiplies the amount of light entering the lens by a factor of 2.

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