# I Aperature, Numerical Aperature and Speed of Lenses

1. May 23, 2017

### Jamison Lahman

I think I understand the relationship between the three, but I would like some feedback. I still am fairly unsure about lens speed and is what I'm mostly interested in.

From my understanding:
Aperture is the total diameter of the lens and numerical aperture is the ratio between the aperture and focus length. The numerical aperture tells the maximum angle a light cone from and object a specific distance can handle while allowing all the light to pass through the lens.

Is the speed of the lens simply the aperture without any type of shutter?

2. May 23, 2017

### Staff: Mentor

Numerical aperture describes the axial cone of light in terms of the marginal ray angle. NA is related to the f-number as follows: $\frac{1}{2NA}$
And f-number is defined as $\frac{f_e}{D_{EP}}$ where $f_e$ is the effective focal length and $D_{EP}$ is the diameter of the entrance pupil. Note that the entrance pupil is not always the same as the aperture.

I believe so.

Hmmm. I'm not sure. If we're talking about the lens itself then I would think so.

3. May 23, 2017

### Jamison Lahman

Wikipedia defines the speed as, "Aperture Lens speed refers to the maximum aperture diameter, or minimum f-number, of a photographic lens."
So it seems like the NA is only dependent on entrance pupil which can vary regardless of the lens's speed. Would I be correct in asserting that lens speed is a qualitative characteristic while the maximum aperture is the analogous quantitative characteristic?

4. May 23, 2017

### Staff: Mentor

No, I think both are quantitative. Also, things get a little muddy since we have to distinguish between properties of the lens and the properties of the system. For example, if a diaphragm is inserted behind a lens, then the speed and NA of the system can be much different than the lens.

5. May 23, 2017

### Jamison Lahman

Hmm. The only lens speeds I've ever heard are slow and fast so that's curious to me.
Can you explain more why that makes it muddy? Because of possible asymmetry in the lens (for instance, one side is flat and the other is extremely curved and the marginal angle doesn't extend the total aperture)? Because the image could be virtual?

6. May 23, 2017

### sophiecentaur

f number is the most common aperture figure that's needed. Having searched the term "lens speed" I found that most links simply described the term as the lowest f number for a particular lens. The aperture of a lens is usually the diameter of the front of the lens - which you can measure with a ruler. The focal length is harder to measure because multiple elements will shorten a lens with a given focal length so that it is not the distance from front of the lens to the sensor element Telephoto lenses can be a fraction in length of their focal length.
If you really want to know the 'light gathering power' of a camera lens then you can use its E value, which takes into account the internal losses too. For movie film cameras, it is important to calibrate all lenses on all the different cameras used in a scene in terms of E rather than f because the exposures for all cameras on the set must be matched. I have never come across an E value for any lens I have bought - but maybe I haven't looked hard enough.

Vignetting is very common in cheaper lenses which can have 'optimistic' claims about their minimum f number. Only the central portion of the image actually gets all the light from the object.

7. May 23, 2017

### Staff: Mentor

What makes it muddy is that the optical properties of a single lens are not the same as the optical properties of a system of lenses and other optical elements (like diaphragms, apertures, stops, etc). So it's important to make that distinction. A stop placed behind a lens may drastically change the optical properties of the system compared to the lens. It can affect the f-number, field of view, numerical aperture, and other properties.

8. May 23, 2017

### pixel

The speed of a photographic lens is given by its f/no. The shutter is not involved in discussing the speed of the lens. The light collected by the camera as a whole would depend on the shutter.

"Numerical aperture" is usually used in discussion of the light collection ability of a microscope objective lens, whereas f/no. is used for photography. This is because of the very different way the lenses are used - up close in the former case, far away in the latter.