# Focal Length vs Angle of View

#### greenjelly

I have some questions about angle of view and focal lengths. I was under the impression that there is a fixed relationship between the focal length of a lens, and the angle of view it provides.

1. That means, for instance, that all 200mm telephoto lenses provide the same angle of view. Is this correct?

2. What happens in the case of a 200mm macro lens? Does it have the same angle of view as a regular 200mm telephoto lens?

3. For a subject of a given size at a given distance, do all brands of 200mm telephoto lenses produce the same image? Does a 200mm macro lens also produce the same image, or does it produce a magnified image?

#### Bob Coutant

##### 12-29-2018
FOV(angle) = 2arctan[d/2f]

d = sensor dimension (usually w. respect to diagonal, but any dimension can be used depending on how you want to measure the angle:smile

f = focal length

#### sylvesterii

Essentially what Bob is saying is that the "Angle of View" of a lens is going to be dictated both by the focal length of the lens and by the sensor size of the camera. Thus a 200mm lens on an FX camera will have a wider angle of view than on a DX camera.

Generally speaking, yes 200mm is 200mm despite the fact that it is a Nikon or a Sigma, a Micro or a zoom. That is with several caveats.

First, "focal length breathing" is when the stated focal length of a lens actually changes somewhat based upon the focusing distance. Thus at infinity the lens is a 200mm lens, but focused at 5 feet it is actually a 180mm lens. The 70-2000 VR II is a recent example where this issue came up.

Second, there is a margin of rounding used by lens manufacturers. I have heard that the actual focal length of the sigma 50 is around 47mm rather than 50. Thus it is entirely possible that different 200mm lenses have slightly different focal lengths.

#### sylvesterii

Also, macro/micro lenses do not "magnify." they only permit you to focus more closely (amongst other things).

#### greenjelly

Thanks Bob & Jan! thanks for the fov formula! I understand the sensor size factor. I am just wondering how a macro lens allows you to cover the entire frame with a small bug, while an ordinary lens of the same focal length would span more area.

#### sambo.

I am just wondering how a macro lens allows you to cover the entire frame with a small bug, while an ordinary lens of the same focal length would span more area.

because Macro glass is designed to focus much closer than regular glass, thus helping you to fill your frame completely with that bug.

#### twistedlogic

Generally speaking, yes 200mm is 200mm despite the fact that it is a Nikon or a Sigma, a Micro or a zoom. That is with several caveats.

According to wikipedia:

"The effective focal length is nearly equal to the stated focal length of the lens (F), except in macro photography where the lens-to-object distance is comparable to the focal length. In this case, the magnification factor (m) must be taken into account:

f = F \cdot ( 1 + m )

(In photography m is usually defined to be positive, despite the inverted image.) For example, with a magnification ratio of 1:2, we find f = 1.5 \cdot F and thus the angle of view is reduced by 33% compared to focusing on a distant object with the same lens.

A second effect which comes into play in macro photography is lens asymmetry (an asymmetric lens is a lens where the aperture appears to have different dimensions when viewed from the front and from the back). The lens asymmetry causes an offset between the nodal plane and pupil positions. The effect can be quantified using the ratio (P) between apparent exit pupil diameter and entrance pupil diameter. The full formula for angle of view now becomes[5]:

\alpha = 2 \arctan \frac {d} {2 F\cdot ( 1 + m/P )"

#### sylvesterii

Interesting. I had no idea that once you got passed 1:1 the effective focal length of the lens would change. Although, I suppose since you can't get past 1:1 with a lens in Nikon's line-up without altering it with tubes, bellows or teleconverters, it sort of is still true of "Micro" lenses.

#### greenjelly

Thanks for the interesting points! Is magnification factor a property of the lens construction, and is it independent of focal length? Is there a formula for calculating effective focal length when using normal telephoto lenses with extension tubes?

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