I think it worthwhile to go over a few numbers and equations regarding eyepieces and their use in classic (and any instruments) as several posts here lately have indicated that a review or (an introduction) would be helpful.
Focal Ratio = the focal length of your telescope divided by the diameter of its aperture. The larger the number, the ‘slower’ your scope; the smaller the number, the faster. Generally (but not always) faster scopes are best suited for wide field, lower magnification views of expansive (and often dim) objects, like DSOs. Slower scopes are often best suited for higher magnification views of brighter targets like planets, the moon, or the sun (under proper and safe filtration of course!). Also, it is important to remember that chromatic aberration (CA) will increase as the F/ratio decreases if you are using a classic Fraunhofer achromatic refractor.
Magnification = the focal length of your telescope divided by the focal length of your eyepiece (in the same units). Handy relationships to remember: the longer the focal length of your telescope, the higher the magnification for any given eyepiece. AND, the shorter the focal length of your eyepiece, the higher the magnification for any given telescope.
Exit Pupil = the aperture of your telescope’s objective divided by the magnification. Generally, you don’t want an exit pupil larger than the pupil of your eye will dilate (around 7mm under very dark skies and maximum dark adaptation, but often less (~5mm) for us older folks. A too big exit pupil is like putting a diaphragm over your objective and stopping it down to where you are loosing benefit of some of its aperture. You also don’t want too small an exit pupil or the views will be too dim. Many seasoned observers consider 0.5mm a good minimum on all but really bright objects.
Okay, here is where the magic comes in! Choose an eyepiece that has a focal length equal to the focal ratio of your telescope. This means that for us classics folks, it is great to have an eyepiece with a focal length of 15 to 16mm, one of 10 to 12mm, and one of 7 to 8mm. This is because the scopes we will most commonly have in or classics collections will be the famous F15 or F16 achromatic refractor, an F10 or F11 achromat or Newtonian, and an F8 Newtonian.
Okay, now why those focal lengths? Because, you will find that if you do the math, an eyepiece with the same focal length as your scopes’ F/ratio will produce exactly the same magnification as its aperture and an exit pupil of 1mm. Add a 2X barlow, and you have doubled the magnification and reduced the exit pupil to 0.5mm, (eg, you are now at or close to the maximum practical magnification unless you have an extraordinary instrument and are viewing under unusually good conditions.
A few examples then:
The common 4.5” (114mm) F8 (912mm) Newtonian: An 8mm eyepiece will give you 114X and a 1mm exit pupil. The 2X barlow (or instead, a 4mm eyepiece) boosts it to 228X and an EP of 0.5mm. That same 8mm eyepiece with a 6” (152mm) F8 Newt will get you 152X and 1mm EP, or 304X and an EP of 0.5mm if you add a 2X barlow.
One more common classic- the nearly ubiquitous 80mm F15 (1200mm) achromat. A 15mm eyepiece will put you at 80X and 1mm EP, add a 2X barlow (or substitute a 7.5mm eyepiece) and you are at 160X with an EP of 0.5mm.
One last magic number to note, each time you settle in your eyepiece barlow combination, (or eyepiece) that yields an exit pupil of 0.5mm, you are precisely at 50X per inch of aperture! Now you see why 50X per inch is the oft recommended practical limiting useful magnification under most circumstances.
You should also consider that adding a 2X barlow doesn’t substantially change the eye relief (the distance necessary between your eye and the eye lense of the eyepiece) of your eyepiece, so an 8mm ortho or Plossl with a 2X barlow will be much more comfortable for many of us than a 4mm.
Oh, and just in case you didn’t intuit it, choosing an eyepiece that has a focal length 5 times your telescope’s focal ratio will produce an exit pupil of 5mm. So if you have an 150mm F5 Newtonian RFT, a 25mm eyepiece will be as low as you want to go in all but the darkest skies (and the best dark adapted eyes). If you want to go up to a 7mm maximum exit pupil, the choose an eyepiece whose focal length is 7 times the focal ratio.
I hope this helps in selecting the ‘just right’ Goldilocks combination of eyepieces for use with your particular instrument. Staying with those that produce exit pupils between 5mm and 0.5mm will hold you in good stead.