Lens physics question

Aperture has nothing to do with images size.
The sensor of the camera does not change size. Only the light hitting the (film) sensor changes.

 

The light we see through a large opening comes in at varying angles (respective to the film plane). When we narrow that opening down (i.e. smaller aperture), the light coming from obtuse angles has a harder time getting through, so we see the same image but less light from the subject is coming in.

 

image size would change if aperture blades were right in front of sensor. However they are much further from it, so.... (the above explanations are absolutely correct)

 

The blades have the effect of making the lens have a smaller diameter. In the very early days of photography the "stop" used to be placed in front of the front element. It was a metal plate with a set of holes cut in it and the photographer choose the hole.

Later optical engineers found a way to place the stop inside the lens but at a specific location where it would have the effect of the old exterior stop. They did it by placing the new adjustable stop in a place in the lens where there is no image plane. It is hard to describe but the are places inside a lens system where any given light ray can be associated with any part of the image

It's clear that in front of the lens this must be true because every point on the subject can "see" every point on the surface of the front lens element. So cutting off some plart of the front element does not cut off some part of the image, it only darkens the image over all. There are other places were this is true too and this is where you can put a diaphram to control the aperture. Dust acts the same way.

Dust on a lens surffce does not cast a shadow, but only blocks light. One other way to think about it is that the dust (or aperture) is so grossly out of focus that it casts it's very soft shadow over the entire image.

 

If this were the case then only the edges would darken as you stopped the lens down. But the entire image darkens. The f-stop has the same effect on light rays from the edges as it does on the center of the image. It has nothing to do with angles. Every point of the subject illuminates every point of the front of the lens. Making the lens smaller simply means that the lens intercepts fewer photons and if you make it larger it catches more of them. It works exactly the same as way a large diameter bucket catches more rain then a smaller diameter bucket.

In fact this is a good way to explain exposure to a new photographer or a kid. "Light is like rain and an ISO 100 sensor needs 1 galon of water, an ISO 200 needs 1/2 galon and so on. Control the amount of water of both how long you leave the bucket outside and how large a bucket you us."

 

It has everything to do with angles - we measure refractive indices by the angle at which the medium changes the light. If the incident angle is severe the light will be intercepted as it passes through a smaller aperture.

 

There is no reason, other than size, complexity of optical design, and cost, preventing physical aperture size from being made larger than focal length. Thus apertures wider than f/1 are possible, as in the examples you pointed out. There is, however, a theoretical geometrical limit beyond which a larger physical aperture will not be effective. As pointed out in a previous post, it is all about the angles. A lens cannot capture from an object point or focus a cone of rays that exceeds 180 degrees. Technically this is equivalent to the requirement that numerical aperture must be less than or equal to one for a lens that is used in a medium with refractive index of one, such as air (see for example http://www.mellesgriot.com/products/optics/fo_2_3.htm). Thus the theoretical limit for widest aperture is 1 / (2 NA) or f/0.5. In practice, apertures between f/1 and about f/0.7 or so are extremely rare due to the size, cost and difficulty of controlling aberrations in the design of such complex optics.

 

What about this lens?

 

That fisheye lens has an angular field of view greater than 180 degrees. Read my comment again. I did not say that FOV was limited in any way. My answer regarding a wide aperture limit was not about FOV, but about the cone of light rays projecting from a single object point, or converging on a single image point. Limits on NA and FOV are determined by different geometric rules (but you probably already know that). :smile: