What does f/4.6 mean in a telescope and how important is this value? In some specifications for telescopes, I saw a value marked as f/4.6. What does it mean exactly, and how important is when it comes to choosing a telescope?
 A: This is the f-stop, f-number, or lens speed of the telescope. It is the result of dividing the focal length of the lens with the aperture of the eyepiece. The wider the aperture, the more light it lets through, and the lower the f-stop number.
The lower the f-stop number, the faster the optics are--that is, if you were to attach a camera to your telescope, the f-stop would help you decide how long an exposure you need to take to get a nice picture of a celestial body. If the f-stop is low, the aperture is wide and lets more light in--so you need a shorter exposure.
A: This is the focal ratio of the telescope: the focal length divided by the aperture. It is mainly of importance in astrophotography, where it determines the exposure time. For visual observers, it's largely irrelevant, the magnification being more important (telescope focal length divided by eyepiece focal length). Telescopes with longer focal ratios are basically easier to fabricate, and may be better optically, but they are also bulkier and harder to mount and use.
A: I disagree with the other answers that say this is only important for astrophotography. Think of it this way, the focal ratio is basically a measure of how steep the light cone is inside the telescope. There are a significant number of ways this impacts even visual viewers.
A longer focal ratio means:


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*A narrower field of view (see less of the sky at once), using the same eyepiece. Quality long f-ratio scopes are sometimes nicknamed "planet killers"

*The scope has a more forgiving "depth of focus" (a wider sweet spot of focus)

*The telescope is typically longer and heavier than shorter focal ratios of the same scope type (folded designs, like catatropic scopes, are an exception). Therefore requires a sturdier, more expensive mount.

*Longer focal ratios have a wider tolerance in design and manufacture. This means that they are usually cheaper (for a similar quality of optics) 

*Longer focal ratio telescopes are more forgiving for lower-quality eyepieces

*Longer focal ratio reflectors are easier to collimate because they have a wider tolerance for error


Basically reverse all of those points, and a shorter focal ratio means:


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*A wider field of view (see more of the sky at once), using the same eyepiece. Depending on the exact f-ratio, these are sometimes called "wide-field" or "rich-field" scopes.

*The scope has a more unforgiving "depth of focus" (harder to get the sweet spot of focus)

*The telescope is typically shorter and lighter than longer focal ratios of the same scope type (so easier to transport and handle, allows a lighter mount)

*Shorter focal ratios have a tighter tolerance in design and manufacture. This means that they are either more expensive (apochromatic refractors) or give less perfect views (achromatic short-tube refractors that show lots of false color)

*Shorter focal ratio telescopes are less forgiving for lower-quality eyepieces, and typically require more expensive eyepieces to get the best views

*Shorter focal ratio reflectors are harder to collimate because they have a narrower tolerance for error

A: As others have said, f/4.6 refers to the focal ratio or f-ratio of the primary mirror of your telescope, which is the ratio of the focal length to the diameter of the mirror.
A telescope with f/4.6 mirror would be considered a fast scope (usually anything under f/6 is called fast).
It is trickier to build a mirror with a fast f-ratio since it needs stronger parabolic correction. (The ideal shape of a primary mirror is parabolic not spherical, but mirrors slower than f/6 need very little to no correction have very little difference between the parabolic and spherical shape).
Hence, if you buy a fast mirror you need to make sure it is from a professional / trusted source.
However, it is easier to build a telescope with a fast mirror because the focal length is shorter, making the whole assembly shorter. That also decreases the weight and simplifies the mounting. It is usually easier to handle as well.
