So early this morning I couldn't sleep and I ended up writing an article on flickr in one of the many "what lens should I buy" discussions that goes on there.  I have noticed, in my days on flickr, that certain pieces of equipment and certain techniques have a following, and often get recommended simply because of the following rather than because the equipment/technique is actually suited to the purpose of the person asking.  In an effort to supply a counterbalancing opinion, I found myself in need of trigonometry.

The Argument

One such "cult" item is the "nifty fifty" (the EF 50mm f/1.8) lens made for Canon EOS cameras.  It is very sharp, very fast, and very cheap ($80).  If you are on a tight budget (or even if you aren't) it makes sense to have one for your EOS camera unless you have a better 50mm prime, or don't need a 50mm prime.

While I will not argue that it is probably one of the best value-for-money lenses, it is not versatile at all, and yet it seems to get hailed as a magic-bullet lens.  I regularly see people making claims like "it never comes off my camera".  And after having used it myself, I can only conclude that these people shoot one type of thing and one type of thing only, or it never comes off because they don't own any other lenses.

There is a certain love affair with the 50mm focal length because it was the standard focal length for 35mm film for decades.  But in the age of digital SLR cameras, things are different for the less expensive consumer DSLRs.  These DSLR's tend to use an image sensor that is smaller than 35mm film.  The APS-C style sensor, or crop sensor, does not render the entire image cast by a standard lens, but only a smaller piece in the center.  This results in an apparent magnification factor of 1.6.  Hence if you put a 50mm lens on a crop-sensor camera, it's like working with an 80mm lens (50 x 1.6 = 80).  The end result is a smaller-than-expected "field of view" (FOV).

On an old Canon 35mm film camera, a 50mm lens has a FOV of 46°.  But on a crop-sensor camera the FOV is a hair under 29°.  This loss of over a third of the FOV means that on crop-sensor cameras the EF 50mm f/1.8 lens has distinct limitations as to how much you can fit in the frame.

Fortunately, on my EOS 5D the 50mm behaves as expected. Because the 5D is a full frame camera, its sensor is the same size as a 35mm film frame.  So I get 46° out of my EF 50mm, just as nature intended.

The "nifty fifty" on crop-sensor cameras is often described as a "portrait lens".  With the crop factor, the 50mm lens behaves like an 80mm lens, and 80mm is ideal for portraits.  But if you want to shoot anything larger than a head-and-shoulders portrait with the EF 50 1.8 on your Rebel XT or 30D, you'd better have a lot of room behind you, because you are going to need to back up... a lot.

But how much?

The Trigonometry

Well that's where the trig comes in (you can skip this section if you don't want to see how I figured it out).  In order for me to say how much, I needed to be able to reliably compute the distance necessary to view an object of a given width.  But how?  I started by drawing a diagram like this one:

V is my viewing angle.  Okay it's not 29° (or 28.98333° which is the actual FOV of the nifty fifty on a crop sensor), but close enough.  The legs of the triangle extending out from V represent the edges of my FOV as the distance to the subject (marked by the dashed line, d) grows.  The base of the triangle (marked as w) is the width of the field of view at the distance d.  Basically this is a representation of the wedge or cone of that falls within a particular FOV, in this case 30°.

I can pick any distance I want for d, but what I really need is a way to say what d should be to accomodate a subject of a certain width.  In other words, to fit a subject 10 feet wide in my viewfinder, how far back do I need to stand with the nifty fifty on my EOS 30D camera? I supposed that given a formula for that, I could solve the formula for the width so that one could also compute the maximum width viewable given a distance.

The triangle depicted above is an isoceles triangle, as both the legs are the same length, and consequently the angles where the legs meet the base is also to the same.  I spent some time looking online for computations for isoceles triangles, but what I was looking for didn't appear (namely, given the length of the base, and the angle of the peak, what is the height or altitude of an isoceles triangle?)

I studied trig over 20 years ago so I remember very little of it, but I did remember there were a lot of simple equivalences for right triangles (that is, triangles where one of the angles is 90°).  And I realized while looking at my diagram that the line I had drawn to represent the distance, bisected V and split the triangle into 2 right triangles, each of which looked like this:

Bisecting V gives me a 15° angle (V'), and a base width exactly half of what it was before (w').  So if I could take a given distance d and come up with a formula for w', then I should be able to solve that formula for either d or w', keeping in mind that V' is V/2 and w' is w/2.

Doing a quick check online I found the two rudimentary trignometric equivalences for right triangles: for either of the angles other than the 90° one, the sin of that angle is equal to the length of the opposite side divided by the length of the hypoteneuse, and the cos of that angle is equal to the length of the adjacent side divided by the length of the hypoteneuse.  Here are those equivalences for the right triangle above:

Sin V' and cos V' I can get with a pocket calculator, and I'm going to pick a value for either d or w' and solve for the other.  I can solve the equation on the left for w' [w' = (sin V') * h] and I can solve the equation on the right for d [d = (cos V') * h], but both of these solutions require me to know what the hypoteneuse of this triangle is.

But in order to get w' from d or d from w' I need to do more work, mostly because I am not going to know what the hypoteneuse is.  I'm only going to be starting with either V' and w' or V' and d.  So what I need to do is solve one of the equations for h, and then plug that into the other equation.  That should give me a formula I that I can use to solve for either d in terms of w' and V' or w' in terms of d and V'.  So I picked the equation on the right.  Solving that for h gives h = d / (cos V').

So I should be able to substitute d / (cos V') in the equation on the left, like so:

Now I'm good.  I know what V' is, I can get sin V' or cos V' from my calculator, and I am going to pick either d or w'.  So now I can solve for either one, like so:

Done, right?  Well, yes, if I want to know what the appropriate distance is for half the width of my subject using a lens with half the field of view.  Now I want to substitute in the equivalences that w' = w/2 and V' = V/2.  In the equation on the right that will put w/2 on the left of the equal sign, so I will multiply both sides by 2 to solve the equation for w.  That gives me:

Okay they probably aren't the cleanest formulas in the world, but they work and let you get the height of an isoceles triangle from its base width and peak angle, or vice versa.  Using these formulas I could handily compute the needed distance for a given width in a given field of view, and this allowed me to present something more concrete than "gee whiz, that EF 50mm 1.8 is awfully confining on a crop sensor camera."

Back to the Argument

So how confining is that nifty fifty?

5 feet wide = 9.7 feet away
10 feet wide = 19.3 feet away
15 feet wide = 29 feet away
20 feet wide = 38.7 feet away
25 feet wide = 48.4 feet away

Pretty confining!  If you are trying to capture 3 people sitting on a couch which is 8 feet long all in one shot, you need to stand 15 feet 6 inches away.  Better have a big living room, or one where there isn't a TV 10 feet from the couch.  Or maybe if you moved the couch outside... that would be cool for an album cover, but for Aunt Bea, Uncle Joe, and Granny, it is probably less so.

Working with the EF 50mm f/1.8 is a good exercise though for learning how to push a lens to do what you need, and it's plain old good exercise, because you're going to be backing up a lot.  You can get that 8 foot couch in shot if you shoot from an angle, but then you will need to stop your aperture down to widen up the depth of field so that everyone will be in focus... which means you can't shoot low light anymore so you might need lamps or a flash.  Or you could give up on that shot and shoot the people individually.

Or, you could simply not get the EF 50mm 1.8 in the first place, if you are not planning to shoot primarily portraits.  If you want to consider the traditional FOV that the great 35mm film artists shot with, you need a lens that gives a FOV on a crop-sensor camera similar to a 50mm lens on a 35mm film camera (i.e. 46°).  The closest bet would be a 28mm lens, like the EF 28mm f/1.8 or EF 28mm f/2.8.  These have a crop-sensor FOV of 47.25°.  With one of these lenses the width to distance figures look like this:

5 feet wide = 5.7 feet away
10 feet wide = 11.4 feet away
15 feet wide = 17.1 feet away
20 feet wide = 22.8 feet away
25 feet wide = 28.6 feet away

Much more reasonable.  And quite interesting how the distance to subject is almost the same as the width of the subject.  No surpise that the 50mm lens became the standard on the cameras of old.

The 24$ Pentax K-Mount to Canon EF-Mount adapter came in the mail today, and when I got home I took out Dad's old Chinon CE-4 camera, removed the Chinon 50mm 1.9 lens and attached it to my 400D using the new adapter.

It would be an understatement to say that I am impressed with the results.

What a terrific piece of glass this is!  If you go on eBay you can buy this very lens for under twenty bucks and yet it takes amazing pictures!  My friends, if you have been considering getting a DSLR but have been put off by the price of the glass, and believe me, there's a lot to be put off by, and you don't mind setting the aperture manually and focusing manually, you may definitely want to consider old manual lenses on a new SLR body.

As for me, well I already have a fast 50mm prime, but I really wanted to see Dad's lens in action again.  I was not disappointed.

As you might recall I decided to sell my old Nikon gear off to Adorama and parlay it into new lenses.  Over the phone Adorama quoted me about $250 for my Tamron lens, and $200 for my 28mm Nikon lens.  The camera body is now worth a pittance (like $30), and there was the 400mm Sigma telephoto which they wanted to examine before giving an estimate on, but I was expecting at least $100 for it.  It was never a great lens but it wasn't total junk either, and it went for $600 when it was new.  So for the whole kit I was expecting $500-$600.

Upon receiving the gear Adorama took over two weeks to get back to me and then (after I chased after them for a couple days) offered me $175 for the entire kit.  I could see from looking at their own used equipment inventory page that they would sell the Sigma alone for almost $400.  Yeah.  So like, um, no.  I told them to ship it back to me on their dime.  They offered $200 if I would consider trading it in on a purchase, but I wasn't biting.  I was planning to finance my 70-300mm f/4-5.6 IS lens with this old kit, but given that the new lens was $550, if I ditched my entire Nikon kit at their offer I'd STILL be $375 short.  Not worth it.

Instead I sold my MtG Online account which had a pretty decent collection of virtual cards in it.  I got $510 for that and that ended up financing my telephoto lens (with which, I am totally in love.)  Meanwhile the Nikon gear came back and got stacked next to my old camera bag, into which I had stored my Dad's old Chinon gear, which my Mom had given to me.  Dad's gear included 2 lenses (of which one is infested with fungus and therefore history) but combined with my old Nikon gear that is four lenses that once took beautiful pictures:

1. Nikon Nikkor 28mm f/2.8
2. Tamron 90mm f/2.5 (for Nikon)
3. Sigma 400mm f/5.6 APO (for Nikon)
4. Chinon 50mm f/1.9

Nikon cameras for ages have used the Nikon F-Mount.  In fact the mount was introduced in 1959 and is still in use today (though it was extended when autofocus came on the scene.)  So as long as one is prepared to use them in a manual fashion, one could attach lenses 1 to 3 to a modern Nikon and go... no additional equipment necessary.  Many camera manufacturers created completely new mounts when moving to autofocus, to howls of disapproval from customers who had invested in lenses, but not Nikon. The other notable exception is Pentax.  The K-Mount was created in 1976 and is still standard on Pentax cameras.  I bring it up because the Chinon CE-4 uses an old K-Mount which means lens #4 in the above list should fit on any modern Pentax camera, although it would probably only function in a manual fashion.

So I began to wonder if I could find adapters that would let me use these lenses on my Canon EOS 400D.  People have been saying for awhile that it is not possible with Pentax K-lenses, until a working adapter was invented awhile back.  But for Nikon lenses the adapters have been around awhile and are available cheaply, so I picked one up from an ebay seller in China for the hefty sum of $7.99 (plus $8.01 shipping) and it arrived the other day... and I spent a couple hours playing Dr. Frankenstein, attaching old dead lenses to my EOS 400D.

		Nikkor 28mm f/2.8: I only tried a few shots with the 28mm.  I was surprised by how hot the colors were from this lens.  I can tell it is a good one and with practice I should be able to get some nice pictures with it.  This is one I'd like to throw on the camera and just go out shooting for awhile with it.  It was fairly wide, and therefore I could stand comfortably close to my subjects while shooting with this lens.
		Tamron 90mm f/2.5: The colors out of the Tamron were also very hot, though not quite as hot as the 28mm.  This and the Sigma are the only large primes I've ever owned, so they take some getting used to.  I found that the body of the lens isn't in the greatest shape, the focusing wheel would sometimes slip and turn a little on its own, so I sort of had to hold it in place.  I really took my time with this lens and did a number of shots.  I did notice a lot of flaring (I was shooting without the hood) so I don't know if the lens has an internal issue, although I did a long exposure low light shot that came out looking just fine. Given the slippery focus, I don't think I'd use this prime too much in the field, but for still life at home where I have a lot of control it still can produce nice pictures.  I'm willing to bet I could send it out to be cleaned and have the focusing ring tightened up.  I may try that... the picture quality is definitely worth it.
		Sigma 400mm f/5.6 APO: As expected this beast was the touchiest of the three.  If I ever end up getting that EF Canon 100-400mm someday, this lens will end up on eBay.  I need to do a head to head test with the 70-300mm I own at some point, but I'm willing to bet the newer lens will win. At 400mm the lens magnifies hand shake extremely, and it was never a very clear lens in the first place.  But I found if I baby it enough (and use a tripod) I can still get some very nice shots out of this lens, like these pretty magenta flowers here which required a half-second exposure even though it was a bright sunny day.  Granted, they were in the shade... but a half second???

All in all it was a successful experiment.  I'm sure I will use the Nikkor 28mm and the Tamron 90mm on my EOS 400D.  The Sigma... maybe, I need to experiment with that one some more.  This was pretty fun, and it was nice to see these lenses in action again.  With no electrical contacts the lenses were strictly manual... manual focus, and aperture had to be set manually as well using the controls built into the lenses.  As far as the 400D was concerned, there was no lens on the camera when I took the test shots you see above.

One note about the adapter though, it is extremely thin and getting it on and off is tricky.  It's probably easier to just buy one for each Nikon lens you are going to use and then simply leave the adapter on the lens (note, you'll need to buy a lens cap for each lens you do this to... once the adaptor is on, the lens cap that came with the lens won't fit.)  I've ordered both a Pentax-K adapter for my Dad's old Chinon lens and an M42 style adapter for possible future use.  (There are some really high quality lenses out there which are made to fit the M42 screw-mount, and they can be had very inexpensively.  I think I may want to try some of those one day... the Carl Zeiss Flektogon 4/20mm springs to mind as does a bunch of Takumar lenses.)

So while sitting around yesterday trying to work from home, aching and dealing with my swollen face, I considered the sort of kit I would need to take quality wedding/portraiture photos.

It occurred to me that if I had 10 grand kicking around, I could put together an amazing kit for doing wedding photography and portrait work.  In a moment of idle dreaming I listed it out on Amazon using their "Listmania" service.  You can see it in great detail here. I don't see how I could come up with that kind of dough unless I sold off my collection of Magic: the Gathering trading cards.  It probably wouldn't get me all the way there, but it might get me far enough along to build a useful subset of the gear.

A serious wedding photographer brings a spare camera body on a job--both because the primary camera could break down, and also because it can make switching between lenses much quicker, so I would want a more serious body to be my primary camera and my XTi would be my backup body.  Then I would need a couple high quality zoom lenses and a flash for the new camera.  That would be the basic wedding kit.

In order to do serious portraiture these lenses plus those I already own would probably suffice, but there is a little more equipment I would need for portraiture, and there is at least one additional lens that would be nice to have for the wedding work, and some flash enhancements that would be good for both:

The 16-35 lens gives me serious wide angle capability for large family shots (not unusual for weddings) and I can use it for landscape work when I am shooting for pleasure.  The muslin backdrop, support system, and clamps would be necessary for decent portrait shots, and ultimately I would probably want a few varieties of muslin backdrop, but for starting out, basic black would be fine.  The OC-E3 would allow me to separate the flash from the camera and hold it overhead or mount it nearby, and the LightSphere would let me diffuse the flash for softer lighting.  Stage two brings the total pricetag to $7,720.  This would be a solid wedding/portrait kit.

The only thing lacking is an even longer lens for very special sorts of situations, and a quality backup lens for the XTi body if I am ever shooting with an assistant and we both need to be in the most common shooting range (20's-70's) at the same time.  That's where stage three comes in:

The 400mm L glass with image stabilization should provide the last conceivable bit of reach necessary for weddings and I suspect for most weddings it wouldn't be necessary.  However it would be a solid lens for wildlife when I am not shooting weddings.  The 28-75mm Tamron gets a lot of respect despite the brand and the price, and as a backup lens on the XTi body, that would be fine.  This brings the total pricetag to $9,509 and gives me enough glass to do almost anything I want.  Yes, there's no extreme length lenses (> 400 mm) but I can't conceive of a use for such lenses that could justify the expense.

The glass listed would cover me for macro, wildlife, weddings, landscape, low light, sports, and portraits (especially when you include the 28mm, 50mm, and 90mm primes I already own).  Looking toward specialty landscape and architectural photography, the only other thing I can think of that would be "nice to have" would be a fisheye lens and a perspective-correcting lens.  That would be the "bonus stage":

The fisheye lens lets you squeeze a lot of lanscape into a single shot by giving the shot a spherized look... here's an example taken with the EF 15mm fisheye.  A tilt-shift lens is a strictly manual focus lens that allows you shift the focal plane in order to correct the perspective and distortion that often results from shooting tall structures from relatively nearby with short focal length lenses.  Here's a sample shot with the TS-E 24mm.  Anyway this would put the pricetag at $11,188, but what a killer kit this would be!!  Ah well... if I win the lottery someday... fun to think about I suppose.

If I sell off my MTG collection and save up my pennies for awhile, the basic wedding kit becomes a distinct possibility. I'll be devoting some serious thought to that over the coming days.

You know... there's a group for everything on flickr...

Here's a little something neat I found on flickr.  Like most big internet repositories, flickr has had a virtual community of photographers that have sprung up around it.  One way it facilitates this is through "groups", also called "pools".  A group is simply a collection of photos that you can submit your photo to.  Typically groups have some sort of theme (like landscapes, cities, cats, clouds, water, or highly specific stuff like "Fitchburg, Massachusetts").  Some groups are intended to help you become a better photographer, in that if you submit a photo, you must critique the N photos that were submitted before yours.  This guarantees input from other people which can be very useful if you are trying something new.

But one of the most interesting groups I've found is called ID Please.  This is a group for submitting photos you took of things you can't identify.  The group members have specialized knowledge, and if they recognize the thing you posted, they'll tell you what it is.  The primary submissions seem to be pictures of flowers, insects, and birds.  But I have seen pictures of all sorts of things go by and get identified, airplanes and vehicles, antiques and apparati, cityscapes and locations, even one person who had taken a picture of something on the ground from the window of an airplane at high altitude and wanted to know what it was.

Since I discovered this group I am rapidly becoming familiar with the local plants and animals in my area.  In exchange for their help, I try to offer information on pictures of birds that are submitted to the group.

All in all, it's pretty neat!  If you've got a picture of something you can't identify, perhaps you should upload it to flickr and submit it to the ID Please group. 

(Or anywhere on the internet really.)  People will find your images, copy them, and use them for their own purposes.

I mention this because I have just heard about  Flickr user "Lara Jade" who recently discovered that a self portrait she photographed when she was 14 years old was used as the cover for a pornographic DVD without her knowledge.  The responses she has received from the DVD company border on the bizarre and betray an extremely warped sense of morality and personal responsibility.

Sadly for Lara Jade, she cannot afford the legal fees necessary to pursue the matter, especially since she lives in the UK and the photo was misappropriated by a company operating in the USA.

Read her story here.

Those of you who post personal or family photos are advised to publish them as "private" photos -- viewable only by people you name as family or friends.  This is not something I've ever worried about on my blog, but I am now wrestling with the idea of marking some of my photo albums as private.  If that happens, anybody who wants to view those albums will need to create a reader account so I can add you as an approved reader.  I haven't decided what I am going to do.  This could be a good opportunity to just switch to Flickr.  I'll have to think on it.