Does longer focal length result in a darker image?

[IanIan]

Hi,

I've found a couple of places on the internet where people have said that the longer the focal length the longer the light has to travel and as it travels it gets weaker.

I don't find this very convincing because we're talking about very small distances which I don't think account for the f-stop difference between a lense when its zoomed and when its not. Something else must be happening to the light!

Any thoughts?

Cheers, I.

[kevinbythebeach]

when u have a wide open shot your camera and lens are getting all the light in the frame...when you zoom in the area is reduced and both get less light....

[IanIan]

Oh, I think its because as the focal length increases, the image get bigger and so the same light is spread over a wider area and thus the overal image gets dimmer.

[McQ]

The ONLY** factor that determines the amount of light that is let through your lens is the f-stop. The f-stop is calculated from both the lens focal length and the physical size of the aperture. In other words, f-stop already takes focal length into account.

However, for a given f-stop, say f/2.8, the physical size of the lens opening gets larger for longer focal lengths. This is why a 50mm f/2.8 lens is much narrower than a 300mm f/2.8 lens, for example. In a sense, I see where these places on the internet are coming from, but they are likely confusing the terminology by mixing up "physical aperture diameter" with "f-stop".

Hope this clears things up.

**the transmittance is also important, but for most purposes this can be assumed to be near 100% or at least negligible compared to the difference between f-stops. Some lenses, like Canon's 24-105 f/4L IS, have transmittance values that mean their f/4 is noticeably less than f/4 when it comes to how much light they let in, but not when it comes to determining depth of field.

[carregwen]

What he said (McQ)

Have a look at this. http://www.uscoles.com/fstop.htm It sort of explains it all.

[IanIan]

when u have a wide open shot your camera and lens are getting all the light in the frame...when you zoom in the area is reduced and both get less light....

Hey Kevin, I wrote my follow up post before I saw yours.

I'm not sure about your theory... Imagine that you increase the focal length of the lense without actually moving it. (In practive I don't think this is possible but it works in the simulations online.) Before and after the focal length has changed, the lense is receiving exactly the same set of light rays.

[McQ]

when u have a wide open shot your camera and lens are getting all the light in the frame...when you zoom in the area is reduced and both get less light....

This is why zoom lenses often have a variable maximum f-stop which decreases for longer focal lengths compared to "normal" focal lengths. However, this *does not* mean that a longer focal length will be darker when the f-stop and exposure time are identical.

[IanIan]

The f-stop is calculated from both the lens focal length and the physical size of the aperture.

Right, so if the physical size of the aperture remains constant, why would changing the focal length change the brightness of the image?

However, this *does not* mean that a longer focal length will be darker when the f-stop and exposure time are identical.

Well thats' the bit that doesn't make any sense! If the exposure is identical then what on earth is the point of giving it an incorrect f-stop value?

[Bill44]

IanIan, unfortunately you will find a lot of twaddle (polite term for outright bulls droppings) posted on the net. It varies from half truths formed from an incorrect understanding of things, through to absolute and complete twaddle.

On a particular forum I followed a discussion regarding the use of a grey card in digital photography. With the rubbish that was posted, OMG it is no wonder that newcomers to photography get confused.

[McQ]

Right, so if the physical size of the aperture remains constant, why would changing the focal length change the brightness of the image?

Mostly because you are reducing the angle over which you are collecting light. Again though, this also means that the f-stop is decreasing as you increase the focal length...

If the exposure is identical then what on earth is the point of giving it an incorrect f-stop value?

The f-stop is in a sense an arbitrary definition, so calling it incorrect is really an attack on the person who designed the convention . Seriously though, the naming convention for f-stop makes photography much more straightforward. You give me any normal lens along with it's f-stop setting, and I can tell you the depth of field (for a give focus distance) and the necessary exposure time (for a given scene & ISO). It's that universality that makes the f-stop so useful.

[Colin Southern]

Would the image end up darker?

Assuming that the camera was in an automatic metering mode (eg Tv, Av, P, Auto), the short answer is NO, because if the light entering the lens dropped (say zooming in on a variable F-Stop lens) then the camera would simply drop the shutterspeed to compensate.

[McQ]

Yes, good point. I was taking camera metering out of the discussion and just speaking to the amount of light reaching the sensor. However, that's likely not what IanIan is referring to. When metering is taken into account the image itself would have the same brightness, but the lens itself will let in less light over a given period if it has a longer focal length (and same physical aperture diameter).

[IanIan]

calling it incorrect is really an attack on the person who designed the convention

Yes I wanted to change it to 'inconsistent'. But I understand now that to maintain the exposure the camera could lower shutter speed to compensate.

Mostly because you are reducing the angle over which you are collecting light.

I'm not quite sure what you mean. My understanding though is that a lens collects the same light from the scene in front of it regardless of the lens' focal length. Its just that a weaker lens results in a larger projection of the scene onto the sensor than a stronger lens. Because the image of the scene formed by the weaker lens is bigger than that formed by the stronger lens, less of the scene fits onto the sensor and it looks like one has zoomed in. Furthermore, because the same light input has been spread over a larger area, the image is dimmer.

In theory I reckon that if a lower powered lens was coupled with a big sensor then it could project the same angle of view as a higher powered lens with a smaller sensor. The larger image would continue to be dimmer than the smaller image because even though its been formed from the same set of light rays those light rays are less dense because they've been allowed to travel further apart.

[will_c]

I'm not quite sure what you mean. My understanding though is that a lens collects the same light from the scene in front of it regardless of the lens' focal length. Its just that a weaker lens results in a larger projection of the scene onto the sensor than a stronger lens. Because the image of the scene formed by the weaker lens is bigger than that formed by the stronger lens, less of the scene fits onto the sensor and it looks like one has zoomed in. Furthermore, because the same light input has been spread over a larger area, the image is dimmer.

In theory I reckon that if a lower powered lens was coupled with a big sensor then it could project the same angle of view as a higher powered lens with a smaller sensor. The larger image would continue to be dimmer than the smaller image because even though its been formed from the same set of light rays those light rays are less dense because they've been allowed to travel further apart.

Yes, a compact camera, for example, has a higher powered lens and a smaller sensor than an SLR, and if the aperture diameter were the same then the image from the SLR lens would indeed be dimmer. But the compact camera's lens also has a smaller aperture. The f-number, being the ratio of the focal length to the aperture diameter, takes into account the fact that the longer focal length SLR lens needs a larger aperture in order to get the same energy per unit area per unit time at the image as the shorter focal length compact lens. In order to do this it makes use of a larger cone of light from every point on the object. So as far as image brightness goes an F/2 lens is an F/2 lens, regardless of its focal length. That's the main point of the f-number system. Of course for a given resolution the SLR can use much larger sensor elements and so get greater sensitivity. The fact that it is the area of the aperture that determines how much light from every point is used, whereas the f-number is expressed in terms of diameter, explains why a stop (doubling) is represented by a factor of 1.4 in the f-number (actually the square root of two), since the area of the aperture is proportional to the square of the diameter.

[JonathanC]

In theory I reckon that if a lower powered lens was coupled with a big sensor then it could project the same angle of view as a higher powered lens with a smaller sensor. The larger image would continue to be dimmer than the smaller image because even though its been formed from the same set of light rays those light rays are less dense because they've been allowed to travel further apart.

OK I'll have a go here.
What Ian says above is completely correct, the bit tht gets missed is the size of the "hole" collecting the light. Lets say the "hole", or front lens element has a diameter of 50mm and do the sums.
For a "weak" lens, say a 50mm lens the image that gets spread over the sensor might include perhaps a tree, a cow and lots of grass. the amount of light getting in is spread past the sensor as well, of course, but we don't consider this.
For the "stronger" lens, say 100mm, we might get just the tree in shot. This would be one quarter of the previous image, getting 1/4 of the light to the sensor, so it would be dimmer.

Here's the clever bit though, the weak lens has a focal length/aperture ratio of 505/50, whereas the stronger one has a ratio of 100/50. That makes the weak lens a f/1 lens and the strong lens f/2, in standard terms.

The camera electronics, or the operator, would need to assess this and change the shutter speed to compensate for the dimmer image. Going from f/1 to f/2 is two stops, so the shutter speed gets halved twice, for the same exposure, staying open for four times as long with the stronger lens than for the weak lens.

Hope this makes sense so far?

What is missing is the correlation between focal length and aperture in most discussions, when its absolutely vital.

For two geometrically similar lenses, where the f/ number is the same but the focal length is different, you would notice that the longer focal length lens has the bigger front element. This is why a 300mm f/2.8 lens is so huge (and expensive) compared to a 28mm f/2.8 lens. The latter only needs a 10mm "hole" to let the light in, but the monster has over 100mm of "hole".

With the "hole" fixed (zoom lens), either the f/ ratio changes as you adjust the focal length, or the lens design ignores some of the front glass at shorter focal lengths to keep the f/ number constant.

HTH

[carregwen]

I have never seen such a lot of confusion trying to explain something quite simple

IanIan, here is the easy explanation.

Get a Pringles tube or any long cardboard tube. Don't eat the Pringles as they are BAD for you (no doubt on that one). Take the ends off. The tube will have a focal length of about 300mm (front of tube to the back where it focuses on your eye) Put tube to your eye and look at something bright. It will be in focus because your eye does that, and you will see the a certain amount of light which to your brain will look normal. You will have a fairly narrow field of view.

Cut tube in half (now 150mm) and repeat the viewing. You will have wider FOV and MORE light (not STRONGER light) will come through, but your eye/brain will compensate (iris closes the pupil more) and it will look pretty much the same. A camera does this on non-manual modes by varying the shutter speed - don't forget that ISO is a factor in this). If you put the camera on manual mode there WOULD be a difference in light with the different length Pringle tubes because you are preventing the camera automatically changing the shutter speed to compensate, which is what your brain does when you view with your eye.

[IanIan]

Hey carregwen, I'm not an expert on this stuff but here's my take on your ideas...

The tube will have a focal length of about 300mm (front of tube to the back where it focuses on your eye)

A tube doesn't have a focal length - a lens does. Focal length is defined as the distance from a lens that parellel light waves which are perpendicular to the lens are focused at. If we consider the end of the tube (or thin air for that matter) as a lens then the lens will have no effect on parellel light waves at all. So I suppose the focal length of the tube is infinite. This doesn't mean that the tube has its focus set to infinity, it means that the tube doesn't do any focusing at all.

Put tube to your eye and look at something bright. It will be in focus because your eye does that

Yes well that's cheating. A camera with thin air for a lens doesn't have your eye inside it to actually do some focusing for it.

Cut tube in half (now 150mm) and repeat the viewing. You will have wider FOV

I think that the reason there's a wider FOV is because the shorter the tube the less of the light arriving at the end of the tube is being absorbed into the inner/outer wall of the tube. This is not how a wide angle lens results in a wider FOV. A wide angle lens (or stronger lens) has a shorter barrel because its capable of bending the light rays it receives into focus in a shorter distance. A weaker lens has a longer barrel purely because the light rays that it collects need a greater distance in order to be brought into focus. When the weaker lens has brought its light rays into focus they just happen to have created a larger image than the image in the wide angle lens. Less of the large image fits on the sensor and so it looks as if one has zoomed in.

The wide angle lens' image is brighter than the weaker lens' image because the weaker lens' image is bigger. Same light -> weaker lens -> bigger image -> less light on the sensor -> dimmer exposure. And so the exposure has to be compensated for either with wider aperture, slower shutter speed or increase in ISO.

What you're describing is a pinhole camera. Despite what I said about it having no focal length, Wikipedia talks about the 'focal length of a pinhole camera'. So I'm still a bit confused on that one.

[Dave Humphries]

Hi Ian,

Firstly, welcome to CiC.

I'm not sure refering to "weaker" and "stroger" lenses is helping here.

Here's my understanding, but other's may differ.
In a lab lens, i.e. say a single convex or bi-convex element, stronger would mean with greater magnification (yes?)

So are you equating that to mean a more telephoto effect, i.e. a longer focal length? and thus weaker meaning shorter focal length = wider angle?

Just my tuppence worth,

[IanIan]

Hi there,

Firstly, welcome to CiC.

Thanks!

I mean...

weaker lens = longer focal length = more zoomed in
stronger lens = shorter focal length = wider angle

[JonathanC]

I mean...

weaker lens = longer focal length = more zoomed in
stronger lens = shorter focal length = wider angle

Well I took it the other way round, weaker lens = lower magnification. Sorry if I confused the issue even more.