Photography 101 - Lenses, Light and Magnification
Photo: Rainer Ebert used under CC licenseThe following post is from Australian photographer Neil Creek who is part of the recently launched Fine Art Photoblog, and is participating in Project 365 - a photo a day for a year - on his blog.
Welcome to the third lesson in Photography 101 - A Basic Course on the Camera. In this series, we cover all the basics of camera design and use. We talk about the ‘exposure triangle’: shutter speed, aperture and ISO. We talk about focus, depth of field and sharpness, as well as how lenses work, what focal lengths mean and how they put light on the sensor. We also look at the camera itself, how it works, what all the options mean and how they affect your photos.
This week’s lesson is Lenses, Light and Magnification
Last week we looked at the basics of the lens. We saw how lenses bend light by slowing it down, how the angle the light enters the lens affects how much it is bent, and how we can use this property to bring light that enters a lens into focus and create a bright, clear image.
Reading Optics DiagramsThroughout this series, I will be using optics diagrams to illustrate various concepts. To help you get up to speed, I’ve written a short introduction on how to read these diagrams. I recommend you pausing the lesson for a moment to learn how to read and understand these diagrams.
The power of lenses
The advantage that lenses gives us over pinhole cameras is twofold: brightness and magnification.
Brightness and f-ratios
We saw in lesson two, with our experiment with the candle and the magnifying glass (Fig 1.2.3), that all the light that entered the lens from the candle was focused into the image. If we substituted a larger lens with the same focal length, then more light would be focused, and the resulting image would appear brighter, but no bigger.
It seems logical that if you double the diameter of a lens, you’ll double the size of the image it makes, but as you can see in Fig 1.3.1 below, that’s not true.
Fig 1.3.1 Doubling the diameter of the lens halves the f-ratio (see below) and collects more light but does not change the size of the image, which is a function of focal length (also see below). Doubling the diameter actually more than doubles the brightness of the image, as the light collecting sufrace of the lens increases rapidly as the radius increases (per the formula Πr2 - pi times the radius squared).
Fig 1.3.2 The f-ratio indicated on a 50mm f1.8 lens.
Fig 1.3.3 The f-ratio indicated on an 80-400mm f4.5-5.6 zoom lens.F-ratio
In photography there’s a handy number used to describe the relationship between lens diameter and focal length: the “f-ratio”. Simply put the f-ratio is the focal length divided by the diameter. In Fig 1.3.1 above we have a lens with a focal length of 50mm and a diameter of 10mm. 50/10=5 which gives us an f-ratio of 1/5 or f5. If the lens was still 50mm focal length with a 20mm diameter, it would be f2.5.
The f-ratio for an SLR lens should always be written on the lens somwhere. Most compact cameras also describe the f-ratio somewhere on the body. The “shorter” the f-ratio, that is the closer it is to 1, the brighter the image the lens will produce. The term “speed” is also used to describe a lens. The word speed in this case refers to how fast the lens will allow the camera to capture an image, given the amount of light available. If the lens produces a bright image, then the shutter can be open for a shorter time to capture enough light to make an image. Thus a short f-ratio lens like f1.8 is considered a very “fast” lens, while a longer lens such as an f8 or f11 is a “slow” lens.
Recalling lesson 1, we learned that a large hole for the light to pass through makes for a brighter but less sharp image. Now that we know about f-ratios, we can connect these two facts together and understand why faster lenses have a narrower “depth of field” - the area which is in focus. We’ll talk more about this in the next lesson, but it’s helpful to connect the dots and see how all these various principles fit together.
Modern cameras allow a photographer to have some level of control over a lens’ speed by adjusting the aperture, we’ll also cover that in more detail in the next lesson.
Magnification and Field of View
Anyone who has played with a magnifying glass knows that, as the name suggests, lenses magnify. The amount of magnification depends on the focal length. The “longer” the lens, the more it magnifies the image. Short focal lengths have the opposite effect, reducing the size of the image.
Fig 1.3.4 All other things being equal, as the focal length of the lens increases, the relative size of the image also increases.
We saw above that f-ratio affects the image brightness. The two factors in the ratio are lens diameter and focal length. So far we have only talked about changing the lens diameter, but with greater magnification you increase the focal length, so you also increase the f-ratio. This means that the more you magnify the image, the dimmer it becomes. Most telephoto (long focal length) lenses have large f-ratios, and are therefore slow lenses. The exception of course are the hugely expensive and very heavy, giant lenses used by sports photographers. These use long focal lengths, and big diameter lenses. These telephotos are not for the casual photogrpaher!
Fig 1.3.5 A macro zoom lens showing magnification factors on the barrel.Photo: Martini Captures used under CC license
We’ve talked about how lenses make the image bigger, and that’s certainly how it appears when you look through the viewfinder, or at the print from a telephoto lens. In reality, because most objects are distant, and the sensor is small, the vast majority of lenses produce an image which is smaller than the object itself. There are some specialist lenses, however, which do make an image larger than the subject. For this to be possible, the focal length needs to be long and the subject close. These are, of course, macro lenses.
Macro lenses will often be described by their “magnification factor”. A lens with a 1:1 magnification factor produces a projected image on the sensor which is the same as the subject. So the image of a 20mm diameter coin will span 20mm of the physical sensor, resulting in an image which will nearly fill the entire frame of a typical DSLR. A 1:1 magnification factor is usually considered the minimum for a lens to be described as a “macro” lens. Specialist macro lenses are often 1:3 or even 1:10 magnification factors, meaning that 1mm across the subject becomes 3mm or 10mm when projected onto the sensor, thus 3 or 10 times magnification.
Field of View
The final variable in this initially confusing balancing act of optics is the field of view. This refers to how much of the world the camera can see. A lens’ field of view depends on the focal length of the lens and the size of whatever the image is projected onto. In the case of digital cameras this is the sensor chip.
Fig 1.3.6 As the focal length increases, the field of view narrows and the image enlarges.
Fig 1.3.7 An example photo taken with an 8mm fisheye on a 1.6x cropped sensor.
Fig 1.3.8 The comparative differences in frame size from compact camers through film and DSLR to medium format.
Fig 1.3.6 makes it obvious that at the wide-angle end, a slight difference in focal length translates to a large difference in field of view. The difference in field of view between a 10mm and 20mm lens is far greater than the difference between 210mm and 220mm. Some lenses can have exceptionally short focal lengths and wide fields of view, such as 12 or 8mm. These are fisheye lenses, so-called because the front of the lens bulges so much it looks like a fish’s eye. These lenses can have a 180 degree field of view, or even greater.
The size of the sensor also contributes to the field of view of a particular lens. In Fig 1.3.6 a particular sensor is shown at different focal lengths. Obviously if the sensor is smaller, it can see less of the image presented by the lens, thus the field of view is reduced and magnification is increased. This is the case for “cropped sensor” DSLRs, and compact cameras.
The “standard” frame size is 35mm, the size of a single picture on a roll of film. Cameras with this sized sensor are known as a “full frame” cameras. Large format film cameras exist with much larger film sizes, such as 150mm x 100mm. Less expensive, or earlier model DSLRs use sensors smaller than a 35mm film frame, and are referred to as cropped sensors. A typical cropped sensor may be described as a 1.6x, meaning that the apparent focal length of a particular lens is 1.6 times longer. Compact cameras use the smallest frame sizes of all, and as such require very short focal length lenses to get wide angle views.
Next Week
Photography 101 - Aperture and stops.
Now that we’ve pulled together the main theory behind the lens and creating an image, we’ll next turn our attention to exposure and how we control the capture of an image. Next week will see the introduction of the exposure triangle, an explanation of “stops” and brightness levels, and a look at the first point on the triangle: aperture.
Homework
- Find out your lenses’ field of view. Using whatever method works best for you (eg a tape measure on a wall), work out the field of view of your camera at the widest and longest settings. Measure it in degrees from side to side. Present photos of your findings.
- Shoot your entire focal range. Find an appropriate subject (eg an urban street or distant tree) and take a series of photos starting at your widest angle and zooming in at say 20mm intervals to your longest zoom. Compile them into a single image and post.
- Exploit magnification and field of view artistically. Take a photo at each extreme of your camera’s focal length range, carefully selecting the subject to take advantage of the magnification and field of view. Share the results here.
- Get up close and personal. This is ideal for users of compact cameras, which due to the optics of a small camera system are capable of focusing very close. Experiment with macro photography and show us photos of the world of the very small. Use macro mode if you have it (usually identified with a tulip symbol). DSLR users with macro gear may also participate.
- If all this is new to you, find an online camera store (for example the Canon or Nikon sites) and browse the lens catalogue. Pay close attention to the lens specifications we have discussed, and see how the shape and form of the lens matches up with these numbers. Look at how long telephoto lenses are, how wide fast lenses are, and how much ultra wide angle lenses bulge out the front.
Resources
- Canon lenses
- Nikon lenses
- Sigma lenses
- Tamron lenses
- Angle of view on Wikipedia
- Interactive focal length comparison on Canon
- Field of view calculator
In addition to posting his Project 365 photos to his blog, Neil also runs a monthly photography project. This month’s topic is Iron Chef Photography - The Fork.
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March 28th, 2008 at 12:49 am
Hi
Please keep on sending us these lessons. They are absolutely priceless. I appreciate each and everyone of them, and enjoy doing the experiments which are really helping me learn the right way.
Being handicapped body wise, I am very slow at doing these lessons and have not yet posted any results. I do understand the concept of what is being explained, and even though I have not posted any results I will try and do my best to upload my results in the near future.
Thank you for having me in this class.
Now for a stupid question. Is it possible for you to give me the link to the forum where I am supposed to send in the url of where I have uploaded. There are so many forums I would not wish to send to the wrong one.
Dot
March 28th, 2008 at 1:56 am
Wow that really brings the first three lessons together and helps join a lot of dots up for me.
The explanation and the diagrams work very well together.
Although with being new to learning these subjects I did have to read through a couple of times for it to sink in!
This course has brought on my understanding of fundamental photography no end,thank you and I’m really looking forward to next week…
March 28th, 2008 at 3:34 am
For simple 1-element lenses the focal-length to diameter ratio applies, but not so for the complex lenses we have on our cameras.
The F-ratio is the ratio of focal length to entrance pupil. For a 1-element lens, the entrance pupil *is* the diameter of the lens. For a complex lens system, elements within the lens restrict the entrance pupil.
http://en.wikipedia.org/wiki/F-number
I point this out in case anybody decides to look at their 14mm lens with its 50mm diameter front element, and then gets confused when they find a maximum F-number of f/0.28 - as I did when I first explored F-ratios d:)
Instead, with a 14mm lens whose wide open f/number is f/2.8, somewhere inside the lens there’s an entrance pupil of 5mm.
These tutorials are awesome. Many thanks, Neil, for taking the time and effort to write all this stuff up for the benefit of all DPSers.
March 28th, 2008 at 3:35 am
I’m going to also say thanks for posting these lessons. I’m developing (boo) my skills behind the camera in earnest this year, and as soon as I figure out how to compile images (photoshop?), I’ll be posting the homework.
Thanks again!
March 28th, 2008 at 4:18 am
Can someone clarify the f-ratio on the front of my lens? I have a Canon S3IS and the front of the lens is printed with “1:2.7-3.5″. What does the 1 refer to and why does the camera list a range that is shorter than what I actually can use (the S3 can have a max aperture of f8?
http://a.img-dpreview.com/news/0602/canon/canon_s3is_frontback.jpg
March 28th, 2008 at 5:05 am
Hi Neil,
very nice tutorial you have here. Thanks a lot for the effort. However I have noticed that all your lens diagrams have a problem with their “definition” of focal length. It is not the distance between the lens and the image.
The focal length of a lens is fixed, it depends only on the material of the lens and its internal and external curvature radius. It does not change when the tree moves closer or farther away from the lens. In all cases the image of the tree does come into focus at difference distances, but never on the focal plane (unless the tree is at an infinite distance). For finding out the focal length, you need to look at the horizontal light rays traveling from the top and bottom of the tree. After passing the lens they bend, and the point where they cross is the focal point. (Focal length is defined as the distance between the lens and the focal point). Afterwards they keep traveling for a while until reaching the plane of the image.
Your diagram in last lesson shows the focal length changing as the tree moves closer. This is not true. The focal point (where the horizontal rays cross each other) stays always at the same place.
In a camera the distance between the lens and the image plane is fixed. This means that if we want to look at things at different distances we need to change the focal length, in order to have them all focus on the same plane. With one lens this is not possible. However cameras have several lenses, and by changing the distance between them we can make the equivalent focal point of the system change position too. The focal length changes so that the image stays in the same place (in your diagrams you are defining focal length as the distance between lens and image, which is fixed for any camera!).
I hope I have managed to explain it. I did not mean to criticize your lessons in any way, I think you are doing a great job and that’s why I’d like to see that it stays accurate.
Thanks again and keep up the good work!
March 28th, 2008 at 6:44 am
Where do I find the diameter number (not focal length)? And is it on the body of the camera, or the lens?
March 28th, 2008 at 6:54 am
This is a great lesson. It’s great to understand some of these relationships, even if it only serves to explain why those telephoto L’s are so expensive! ;-)
thanks!
ds
March 28th, 2008 at 10:51 am
Stephon wrote:
“Can someone clarify the f-ratio on the front of my lens? I have a Canon S3IS and the front of the lens is printed with “1:2.7-3.5″. What does the 1 refer to and why does the camera list a range that is shorter than what I actually can use (the S3 can have a max aperture of f8?)”
Hi Stephon,
1:2.7-3.5 is a standard way for lens manufacturers to say “this lens has a wide-open f-ratio (or f-number, same thing) of f/2.7 through f/3.5.
Why does it have a minimum range instead of a single value? Zoom lenses don’t have a fixed focal length (nor a fixed entrance pupil). Your lens’s focal length can zoom from 6mm to 72mm (from your picture). So for your lens the wide-open aperture at 6mm is f/2.7, and as you zoom from there to 72mm the wide-open aperture decreases to f/3.5.
Of course, if you choose a narrower aperture like f/8, it can do that throughout the zoom range. The markings show you the wide-open aperture range so that you know how fast the lens is.
March 28th, 2008 at 11:00 am
ecm wrote:
“The focal length of a lens is fixed, it depends only on the material of the lens and its internal and external curvature radius. … Your diagram in last lesson shows the focal length changing as the tree moves closer. This is not true. The focal point (where the horizontal rays cross each other) stays always at the same place.”
I think the point Neil’s making is that if you change the focal length, then the field of view changes and the image on the sensor plane gets smaller.
I think we’re to imagine that the lens is being changed between each slide to one with a different focal length. In the animated diagram, he even shows the shape of the lens changing between slides. (I hadn’t noticed that before, good attention to detail, Neil!)
Also, he’s not showing the tree moving closer in any of the diagrams. In each diagram, the object tree is the upright one on the left and the image of the tree projected on the sensor plane is the upside-down one on the right.
Hopefully that clarifies the lesson a bit.
March 28th, 2008 at 12:56 pm
Almost done w/ the homework. Where do we post? =)
March 28th, 2008 at 1:12 pm
NormMonkey, the diagram with the tree moving closer to the lens is in the previous lecture, Fig 1.2.6.
And there is no problem with imagining a different lens for each slide. The problem is that in all cases the distance between the lens and the image is labeled “focal length”. And that, simply, is NOT the focal length.
March 29th, 2008 at 4:52 am
Nice set of articles from Neil. But I agree that the diagrams are in fact a little misleading.
I have a few questions though for ecm:
1) ecm wrote: “In all cases the image of the tree does come into focus at difference distances, but never on the focal plane (unless the tree is at an infinite distance)”
What exactly do you mean when you say that the image never comes into focus on the focal plane (film)? Isn’t the whole point to get it focused on the focal plane? Or did I misunderstand what you wrote there?
2) When you try to take a picture of an object at infinity (e.g the sun) all light converges to a single point - the focal point. Where does the focal plane need to be? I.e can the focal plane come anywhere after the focal point (or to paraphrase that – does it make sense to, or is there such thing as, “focus” an object at infinity)?
3) ecm wrote: “In a camera the distance between the lens and the image plane is fixed. This means that if we want to look at things at different distances we need to change the focal length, in order to have them all focus on the same plane.”
This is interesting. Does this mean that the image size, in a real camera, is always fixed, and doesn’t change whether I take a nearby or far away object? (as opposed to all those diagrams on optics showing that the image size changes when the distance of the object - or focal point, hence lens - is changed)
4) ecm wrote: “However cameras have several lenses, and by changing the distance between them we can make the equivalent focal point of the system change position too.”
I never really thought about camera lenses this way. Thanks ecm for your feedback.
March 29th, 2008 at 6:18 am
I do a lot of local rock band photos. What is best lense for low light clubs and fast moving band member subjects? i have a canon rebel cuz it takes the hard knocks pretty well and am using the standard lense that came with it. I am just using a lot of settings to see what works best but want to get a better lense. any help/opinion is appreciated. P.S. I am having fun too!!!
March 29th, 2008 at 9:49 am
Thanks everyone for your positive and thoughtful comments! I especially appreciate the folks who are helping to spot inaccuracies or points that aren’t as clear as they could be. I am very willing to make corrections to this series, and if some points need further explanation, then I’d be happy to revisit them in a later post.
I want to remind everyone that I’m not an optician or camera designer. Just someone with a passion for photography and science, and who did pretty well in high school physics. Oh and I’ve also made my own 200mm diameter reflecting telescope from scratch. So I’m not an “expert”, but I probably know more about how photography works than the average newcomer to the hobby.
I intend to be involved in the discussion to improve the series accuracy, but I am quite busy this weekend. Also, I think the comments on a post isn’t the ideal place to work on this topic, so I’d like to suggest we start a thread on the wonderful DPS forums. I won’t be able to do so (heading out the door in 10 mins), but if someone else would like to start a “Refining Photography 101″ thread and link it from here, I’d appreciate that.
Remember, I don’t mind being told I’m wrong, I want to make the Photo101 resource as accurate and useful as possible, so I appreciate your input! I look forward to joining the discussion soon.
March 29th, 2008 at 5:08 pm
Hi Neil
Please can you advise where I can see or download the previous lessons
Regards, Sue
March 31st, 2008 at 3:54 am
Here’s my homework attempt on the macro shoot:
http://flickr.com/photos/tsaiek69/2373853213/
Honestly - I didn’t notice the 2 orchid flowers all these years… haha.
March 31st, 2008 at 8:37 am
My lessons 1 and 2 uploaded.
Dot
http://www.flickr.com/photos/25173793@N04/
March 31st, 2008 at 12:00 pm
Hi! Two of the assignament:
a) Macro photo:
http://farm4.static.flickr.com/3211/2375111693_e84ecb5541_b.jpg
and
b)Entire focal range:
My cammera is a Lumix fz8, with focal range from 6.00mm to 72.00mm (eqiv 35mm: 36-432mm) I shooted seven photo with aperture 3.6, resize to 800×660 and merge them in a file. You can see it at
http://farm3.static.flickr.com/2156/2375111689_f18e40e15a_b.jpg
Since I have not a pro account, also I upload the file at full size to imageshack
http://img168.imageshack.us/img168/3258/101less3nb7.jpg
April 3rd, 2008 at 6:34 am
Here’s my attempt at the homework:
http://thephotographerblog.com/140/what-does-f-ratio-mean/
Thanks
April 5th, 2008 at 6:37 am
My lesson no 3 lenses and light is now uploaded
Thank you for another interesting assignment.
My camera is a Canon XTI 12 with a 18-55 mm lens.
Dot
http://www.flickr.com/photos/25173793@N04/
April 6th, 2008 at 8:54 pm
In answer to Ryan Slander’s post:
I’m very sorry I didn’t answer before, but I have been away last week and just got back yesterday. So I don’t know if you are still reading this post, but just in case, here it goes:
I see there is some misunderstanding on what “focal plane” means. The focal plane is the plane where parallel rays hitting the lens converge. This plane is fixed, all parallel rays always converge at different points of this same plane. If your parallel rays happen to be perpendicular to the lens, they will converge on a point on the axis, the “focal point” (part of the focal plane). The distance between the focal point and the lens is the “focal length”.
If you have several lenses, once again the focal plane of the system is defined as the plane on which parallel rays hitting the first lens converge after going through all lenses, and it is also fixed. (Its position can be computed from the focal distance of each lens and the distance between them).
However the focal plane is NOT where the image is focused. In each situation, the image is focused at a different distance from the lens, depending on the distance between the lens and the object we are photographing (there is a simple equation that allows you to calculate where the image will form, once you know the focal length and the distance to the subject). That plane where the image is focused is what I have been calling the “image plane”, and it is NOT FIXED.
In a camera, the film is not placed on the focal plane. We want the image to focus on the film, so the film has to be placed on the “image plane”. Unfortunately, the image plane changes positions. The solution: instead of using just one lens (with a fixed focal length), use several, and change the position of the lenses among themselves. That way you can in fact change the focal length of your system, in such a way that you can get the image to always focus on the film. That’s what you do when you are focusing your camera: changing the distance between the lenses.
And the last point: yes, the size of the image does change, as you well know from your camera. It depends on the size of the subject, the distance between subject and lens, and the focal length of the system. By getting close or farther away from your subject you change the size of the image you get. Also by changing the lens of the camera you change the focal length of the system and therefore the size of your image. The only one thing fixed in your camera is the position of the film! That’s what I said on my first post: the distance between lens and image cannot change. The size of the image certainly can.
I hope this answers your post, and sorry once more for taking so long. :-)
April 8th, 2008 at 1:15 am
my macro shot - last lesson is in my DPS folder
http://farm3.static.flickr.com/2136/2386907847_4d224004f5_m.jpg
April 9th, 2008 at 1:37 am
ecm, thanks for rather complete answer. I think I have a clearer picture of how things work now. I feel that knowing such technical internal details, while not necessarily required to take good pictures, can eventually make you a better photographer by knowing how to make the right choices. I’d like to learn more about such details, particularly about optics and lens, is there any particular book, within the bounds of photography, which you would recommend?
Neil, your articles are great and I like the diagrams. I think if they’re complete and accurate, they can form one of the better online references. The truth is here isn’t a decent online reference that covers what you have presented, and what we have discussed in this thread so far. Most articles I’ve read only paper over the technical details. I know that not many people will be interested in the technical details, but I think it is possible to structure things so that they can easily skip parts they find aren’t immediately necessary.
I hope you continue penning the rest of the articles, and perhaps alter the current ones.
April 9th, 2008 at 3:06 am
Glad to be of help, Ryan. :-)
I’m afraid that most of the books on optics I’ve read are well outside the bounds of photography… I think the best choice would be to look at the chapter on optics and lenses on a basic high-school-level physics book. It will have all the information you could ever need and it shouldn’t be too difficult to follow. Also you could check the wikipedia…
If you are really interested in these things, there is a great non-technical book I can recommend. It does talk about photography and lenses, but also goes well beyond that to discuss the nature of light, the functioning of our eyes, optical illusions, holography… It’s called ‘Seeing the light’, by David R. Falk, Dieter R. Brill and David G. Stork. It’s probably more than what you are looking for, unless you really enjoy this stuff. Or you could read only the chapter on photography, which I believe is self-contained.
April 14th, 2008 at 3:21 am
Hi
Since I have not received anything since march 27
I was wondering if the lessons are still going on?
The lessons were well written and fun to do and it would be sad to find out they have been cancelled, and I am sure others would feel the same way.
If they have been cancelled please accept my thanks for
what I have learned in such a short time.
Dot
April 14th, 2008 at 9:49 am
Hi Dot, thanks for your comment. My apologies for the gap in the lessons. Unfortunately my wife injured herself two weeks ago, and has needed my constant care since. You can read some more details in this forum thread: http://digital-photography-school.com/forum/showthread.php?t=15251&highlight=photography+101
So don’t worry, the lessons will return, I just can’t give a reliable estimate as to when. Thank you for your patience!
April 18th, 2008 at 11:53 pm
Sorry to hear about your wife Neil, I hope she’s up and around again soon!
I was also wondering about the lessons, I’m very glad to hear they’ll be continuing
April 22nd, 2008 at 2:22 am
Same here. May she get well soon : )