Edmends Family History - edmend
One important variable you forgot to ask about is shutter speed. This is the length of time of the exposure. A fast shutter speed (e.g. 1/250th of a second) will 'freeze' the picture, while a longer (1/5) will give you motion blur in the image. By increasing the shutter time, you can use a smaller aperture or a lower ISO setting.
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A typical day time scene requires about f/8 at 1/100th second at 100 ISO for correct exposure. Values are adjusted above or below these settings as light varies.
An oldie but a goodie - you won't see many f0.95 lenses! Photo: 1960's vintage Canon 7 with Leica M39 lens mount and 50mm f1:0.95 lens!
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What the above says is that the light gathering power of a lens increases with diameter (actually proportional to diameter squared) and decreases linearly with increasing focal length. This result is actually reasonably intuitive if you draw a picrure of a lens which is pointed at an evenly illuminated surface. Lens frontal area directly affects light input. Focal length will affect the angle that the lens system "sees" and the area decreases as focal length decreases.
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So brightness ratio between two brightness levels X and Y = 2 ^ (EVx - EVy) where 2 ^ means two to the power of. eg 2^3 = 2 x 2 x 2 = 8, 2^5 = 2 x 2 x 2 x 2 x 2 = 32
This is a very broad question, and I'm tempted to suggest that you buy and read Scott Kelby's Digital Photography book series. It's not the most technical series, but it gives you a nice introduction and tips for taking photos.
ISO was (is) the sensitivity of the film in a film SLR. In digital SLRs it's the analogue and digital amplification in the sensor. It's a number that describes how much light the film/sensor need to correctly expose an image. A low ISO will require more light. If you increase the ISO you can have a smaller aperture and shorter shutter time, and still get a correct exposure.
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Aperture is the 'size of the hole' in the lens. This controls how much light that comes through the lens. A large aperture (denoted with a small f-number) will let more light through the lens. The aperture is also responsible for changing the amount of bokeh in an image. Larger aperture means you can use lower ISO and shorter shutter times.
Focal length does not enter the equation directly but is indirectly related by the fact that f = focal_length / diameter So focal_length = f x diameter diameter is diameter of lens opening.
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In practice you work with ISO, shutter speed and aperture to control exposure for a given brightness or EV level and focal length is taken care of for exposure purposes. Focal length has an extremely importnt effect on several inage attributes, but that's a subject for another question.
Light input changes with 1/f^2 where f is aperture f number. This is because the f number relates to the diameter of a lens but area varies as diameter squared. An f number is often written as eg f8 or f(8) or f/8 but is properly f1:8 or f1/8
Here's a great website with an interactive simulation that will help you learn how these factors interplay when determining the exposure, depth of field, etc., of your photograph: http://camerasim.com/camera-simulator/
To get the correct exposure you need to balance ISO, aperture and shutter speed. Most cameras will do this automatically, but with a SLR you can normally also have manual control over one or more of these variables. This gives you more control and "artistic" freedom.
Many modern cameras can manage most or all of thes parameters for you. As you get used to their affects they become much less challenging to deal with.
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Focal length translates into field of view for a given camera. A long focal length will give a narrow field of view, while a short focal length will give a wide field of view. A short focal length will be similar to 'zooming out' on a compact camera, i.e. you can capture more of a scene.
Light into camera changes linearly with exposure time or inversely with fractions of a second of exposure. eg 0.5 second exposure allows 2 x as much light as 0.25 second exposure. 1/4 second exposure allows half as muchlight as 1/2 second exposure.