I want to be able to photograph the dome of St Paul's cathedral from King Henry's Mound in Richmond Park. Would a telephoto or zoom lens be the best, what focal length/zoom would be the best for maximum detail? The distance between the two is ten miles.
Note: I answered the 'question within the question' rather than the stated title. For the title as it stands [stood, it's now been edited], see What is the difference between a telephoto lens and a zoom lens?
At 10 miles across central London, you're not going to get detail, you're going to get lots of blue haze, even on a clear day.
I can't see St Paul's from here, even though it's about 10 miles away, it's too flat between here & there - however, this is a quick test shot of the farthest thing I can see sticking up into the sky.
This delightful piece of architecture is about 1 mile from me & already is starting to blue & lose sharpness.
It is also bigger than St Paul's dome, if somewhat less photogenic.
Clarity aside, you'd need a very long lens. The above picture was taken with a 300mm lens, I already needed to crop it out from this so we could tell it was meant to be the main subject.
pics are shrunk down, not worth full detail.
&, yes, I know it's not straight ;)
& by pure coincidence of geography, even if I could see all the way to St Paul's from here, that darn building would be right in the way.
Admittedly, I am shooting with the sun at my side not at my back, but I'm shaded so that's not veiling flare you're seeing. From Richmond if you waited til mid/late afternoon you would get warmer lighting with the sun at your back.
You would also get heat distortion in summer.
This might be a better prospect for a clear winter's day shoot.
'Best' is a subjective term. The cathedral is 365' tall and 518' long.
Field of View Calculation
You can use a field-of-view calculator (in this case a dimensional field-of-view calculator) such as this one: Photography Calculators
For the ten mile distance, I'll just round that to 50,000 feet (it's actually a little longer) and plug in some numbers.
We need to know what type of camera you have (specifically the sensor size) but I assumed a full-frame camera.
When I plugged in a 3000mm lens (really a telescope) it provided a dimensional field of view of 400' x 600' -- which would frame out the cathedral nicely. But this means you need a telescope -- specifically a 12" f/10 SCT (Schmidt-Cassegrain Telescope) such as one of these: LX200 ACF - 12" f/10 (OTA Only)
You would also need a way to mount it ... I believe this optical tube includes a Losmandy style dovetail rail -- that's one of two different industry standard mounting rail types used by telescopes). The weight of the optical tube is well beyond what a photographic tripod can support (even a beast of a photographic tripod will likely not handle this much weight). Even an extremely tiny vibration will cause massive image shake at this focal length -- the mount must be rock solid.
Back to the idea of 'best' ... since you will never find a camera lens in this focal length (side note: Canon once made an extremely limited edition run of a 1200mm f/5.6 lens. That lens sold used for $130,000 USD at B&H Photo a few years back. I assume that price range is pretty much out of the question and it's only 1200mm ... less than 1/4 of the focal length you'd probably want if using a full-frame camera. But if using an APS-C camera then around 1800mm would probably be pretty good.) A SCT is a type of catadioptric telescope (catadioptric scopes are also sometimes called compound telescopes because they use both lenses and mirrors to focus the image). Light starts focusing when it hits the corrector plate (a thick piece of glass on the front of the optical tube that has a flat front face but a slightly curved back face. This corrector plate starts bending light in toward the primary mirror at the back of the instrument. The mirror is spherical -- which is normally not a good thing because it results in a spherical aberration problem where it is unable to focus light. This is the real purpose of the corrector plate (it compensates for the spherical aberration - and allows the telescope to use the spherical mirror which is a bit less expensive to manufacture). That primary mirror bounces light forward to a smaller secondary mirror which is mounted back at the front of the telescope in the center of the corrector plate. Finally that light is bounced backward again and through a hole in the center of the primary mirror (so the mirror is basically a donut-shape) where the camera is mounted.
This design results in a reverse vignette where the image is slightly dimmer in the center (some post-processing would be needed to correct for that).
Also... at a 10 mile distance ... you have to image how much heat is rising off the surface of roads and rooftops. This will result in heat currents which distort the image ... especially if you shoot this on a hot day. You would want to shoot this in the very early morning before the land has a chance to heat up -- but I think that puts the sun behind the cathedral and might mean you are getting a silhouette of the cathedral. Anyway... if you can shoot this on a clear cool day you will probably have less of an issue with thermal distortions.
Let's use this image from an article in Guardian about the Manhattan Loft Gardens tower violating the London Plan (prohibiting buildings from ruining the view of St. Paul's from several key locations in the city, including from King Henry's Mound) as a reference for measurement:
Image from The Guardian, St Paul's not consulted on development that mars cathedral view.
The image is 903 pixels wide. I measure the diameter of the dome to be 140 pixels. According to Wikipedia's article on St. Paul's, the dome has a diameter of 34m. Using that as a measurement, I calculate the field of view of the image at St. Paul's distance to be 34 m * (903/140) = 219 meters wide.
Using the equality of ratios of similar triangles, D/WFoV = ƒ/dsensor, where D is the distance to a photographed object (at least 16 km in this case), WFoV is the width of the field of view at that distance (219 m in this case), and dsensor is the width of the camera's sensor (I'm going to use 36mm, the width of the standard full-frame image sensor), and solving for ƒ, I calculate that the 35mm-equivalent focal length of the above image is over 2600mm.
Now, the image from the Guardian article is 903 by 542 pixels, meaning it was almost certainly cropped from a larger image. But it's an example of what is possible under good conditions.
So you could possibly get such an image from an extreme superzoom bridge camera from something like a Nikon P1000, which has a maximum focal length of 3000mm (35mm full frame equivalent field of view). But see this question regarding its image quality: Nikon Coolpix 1000 - how to decide if it's a 'smarter' option than a good long lens?
From this article, Can you really see St. Paul's Cathedral from Richmond Park?, here is the view of the cathedral viewed from the installed telescope at the park (probably captured with a mobile phone):
view of St. Paul's Cathedral through observation scope at Richmond Park. From Lookup London
You need at least 2600mm focal length (35mm full frame equivalent) to achieve similar magnification as the first image. That can only be feasibly (i.e., at reasonable cost) with a superzoom bridge camera like the Nikon 1000, or by mounting a camera to a telescope.