What's the useful magnification for a scope with 70mm objective lens?

Question

Some of the spotting scopes which are e.g. 70mm claim to magnify terrestrial objects at 75x. But yet they cannot produce sharp and clear images at even 30x-35x.

While 90mm scopes can do a better job than them but still they stop producing clear view at higher magnification.

So, I want to know is there a formula from which I can estimate (if not accurately tell) their useful magnification at which they are able to focus objects?

I came across this:

Magnification = Focal length / Eye piece focal length

But not sure if that works for what I am asking.

Answer 1

I make telescopes and telescope optics (mirrors). The question is actually pretty complex. I get it a lot, because most people believe magnification is the end-all-be-all of telescopes, but reality is a little different. Here's what I mean by that:

You are correct that the actual magnification of the instrument (how much bigger the image is, compared to the object) is given by the formula:

M = F / f

M = magnification
F = focal length of the objective
f = focal length of the ocular (eyepiece)

The formula seems to suggest that you could get near-infinite magnification from any telescope by just reducing f, the focal length of the ocular. And it's technically true.

But the question is - how much can I increase magnification before it's too much to be useful?

When you zoom into an image with Photoshop, at some point you start seeing the pixels; any zooming past that point does not reveal more details. Telescopes do not have pixels, but the image the objective provides does not have an arbitrary amount of details - just like with Photoshop, arbitrarily increasing magnification with a telescope past some point will only give you a messy blur (not pixelated, just blurry).

So how much is too much? It depends.

If you had perfect optics, used in perfect conditions, then the maximum useful magnification would be:

Mu = 2 * D

Mu = maximum useful magnification
D = diameter of the objective in mm (a.k.a. aperture)

So for an instrument with a 75 mm aperture, the maximum useful magnification is around 150x. If you increase magnification past this point, the image is bigger, but it also gets progressively more blurry, so no additional details are revealed. But those are ideal numbers.

In practice, optical elements (lenses, mirrors) are not perfect. Only the most expensive instruments have optics that are anywhere near perfection. Imperfections add to the blur.

Even with perfect optics, if the telescope is not perfectly collimated (the lenses and mirrors are not perfectly aligned), that reduces performance too. Most refractors are collimated from factory and need no adjustment, but some cheap refractors may not be perfectly collimated. Other instruments such as dobsonian reflectors need periodic tuning to redo their collimation. When the instrument is miscollimated, the maximum useful magnification is reduced.

The atmosphere is turbulent. This is called "seeing" in astronomy. When seeing is bad, extra blur is added to the image, and you have to dial down the magnification.

Finally, magnification is not the ultimate parameter of a telescope. When you buy a car you don't ask the dealer "what's the fastest car you have?" You adjust the speed of the car to the conditions: drive at one speed on the freeway, at a different speed in a residential neighborhood, and at yet another speed in the parking lot at the local grocery store. Same with telescopes.

Some objects require a lot of magnification - things like Mars at opposition, or certain double stars, or small craters on the Moon, these all benefit from the highest magnification you could get. But objects such as Jupiter are better seen at more like a medium or medium-high magnification (Jupiter is low contrast so too much magnification washes out detail in most cases - but not always). And then there are nebulae and clusters which are better seen at low magnification. Horses for courses.

---

So what's the actual answer?

Well, you have the upper limit set in stone: 2 * D, or 150x for a 75 mm scope. But that's more like a theoretical bound. In practice the actual value will rarely be equal to that, usually will be a little below it, and sometimes much below it.

And then you have to choose your magnification based on the actual object you're observing: high, medium, or low.

This is why for experienced astronomers magnification is just a number. They've learned to adjust the instrument to the local conditions, to the object being observed, and even to the characteristics of the observer (younger folks tolerate very high magnification better than older ones - something to do with the narrow size of the beam of light exiting the scope at high magnification, then hitting floaters and other defects that accumulate with age).

This is why most people end up with a handful of eyepieces, and choose the best one depending on each case.

Answer 2

You are correct that magnification is the Telescope Focal length / Eye piece focal length.

For an F/10 70 mm refractor, the focal length is 700 mm. A common 20 mm eyepiece will get 35x.

With excellent optics, a good rule of thumb is the maximum useful magnification is about 1.5x the telescope's aperture in mm. So an excellent 70mm F/10 refractor might be useful up to 105x, which corresponds to a 7mm eyepiece. If you have a fast, F/5 spotting scope, the maximum magnification would come with a 3.5mm eyepiece; eyepieces with such short focal lengths tend to be hard to use.

Very cheap telescopes may have misaligned or badly figured optics, however, and the maximum useful magnification may be much lower. To get maximum performance, the eyepieces have to be high-quality as well. Spotting scopes tend to have lower focal ratios so they can be more compact; this requires more strongly curved surfaces on the lenses and makes them harder to figure correctly. All telescopes, regardless of price, need to be correctly aligned to get good performance.