The scopes can be dialed to a specific range. This changes the angle that the scope points relative to the barrel, so that the arc of the bullet (gravity pulls down on the bullet as it moves through the air) meets the line of sight of the scope at the prescribed distance. The higher the range, the lower the scope points, so the bullet has to drop further (meaning it flies farther horizontally) to meet the sight line.

The barrel and scope are not parallel. When the scope is perfectly horizontal the barrel is pointing slightly up. So at a set distance from the rifle the bullet will hit what the shooter is aiming for. But the bullet will also drop due to gravity over time so at a distance further away it will also hit. This is why it is so important for the shooter to get the distance right and then set the scope to that distance. If the target is closer then he thinks it is then he is going to hit high, and if the target is further away then he thinks he is going to hit low.

Scopes are zeroed in at a specific distance. You can choose what that distance is. Say 200 yards. You then go to a range and adjust the scope so that the round is hitting the target at 200 yards exactly where the crosshairs are aimed.

Then, most scopes have mil lines across the crosshair lines. Based on the ballistics of the specific ammunition you are shooting, use can use those mil lines to adjust for bullet drop and windage.

Training. No scope (or hard sight) is 100% accurate at all ranges, because bullets don't travel in a straight line. Gravity will always have an effect. Bullets actually travel in an arc. Usually leaving the barrel (most notably in long guns/rifles) at a slightly upwards angle, and then start falling after a bit. Like this --

https://ke-courses-production.s3.amazonaws.com/asset_files/production/3766/attachments/original/muzzleloader-trajectory.jpg

And experienced/trained marksman (hunter, sniper, etc) knows how to compensate for this at various ranges

While the scope and the barrel may look parallel to each other, they're actually set at a slight angle to one another.

The scope is aligned in such a way that it essentially points horizontally. The barrel, however, is at a slight upward angle. This means the bullet, when fired, will arc upwards and descend in a ballistic arc. With a properly sighted scope, the bullet will intersect the scope's line of sight at known intervals.

This means if your scope is zeroed at 100 yards, and you aim carefully at the center of the target and pull the trigger, the bullet will actually rise until it is close to the line of sight (or above it, depending on the caliber), and then fall the light the target at the point of aim.

It's kind of hard to conceptualize because most arcs we're familiar with are very pronounced. The bullet follows an arc as well but it is very very flat. When you think of the flight path of a bullet in this way, and the scope as a horizontal line, where the two lines (the bullet's path and the scopes line of sight) intersect is where the bullet should go -- assuming the scope and rifle have been sighted to one another.

The handy part about this setup is that the scope can be deliberately adjusted off center by the shooter -- this allows the shooter to compensate for different ranges. If you know for instance, that your bullet drops one inch for every 100 yards it travels (ignore for a moment that this implies a linear path), and you know your target is 600 yards away, you can "misalign" your scope in such a way that it shoots high at 100 yards, but on target at 600. This is what shooters are doing when they're turning the knobs on a scope -- adjusting the crosshairs for both windage and elevation. This way they can put the crosshairs directly on the target instead of having to compensate manually.

I believe real scopes also have the ability to dial in a wind which adjusts the horizontal direction of the scope--or maybe they just manually move over a couple lines.

Bullets fly in arches, they are pulled down by gravity. If you would fire a bullet horizontally over a flat surface and at the same time drop now from the same elevation it will hit the ground at the same time.

the result is the scope does not look parallel to the barrel, the barrel will point slightly upwards if you aim horizontally. It looks like https://qph.cf2.quoracdn.net/main-qimg-20f8f9b2aa7051df653d04e40e2233c2.webp The image uses rear and from irons sight, a scope will create a line of sight the same direction as an iron sight

You zero a sight so the bullet trajectory and the line of sight are at a specific distance. Sight for rifles usually have an adjustable rate setting that is calibrated for the rifles and ammunition so the line of sight is changing relative to the barrel the correct amount so they intersect at the new distance.

So if you zero the rifle with so, for example, the 100-meter setting hits the line of sight at 100 meters when you then change the setting to 200m the bullet should hit the line of sight too. If the range is incorrect the bullet will hit above or below where you are.

If you can hold a weapon vertically all the time the distance the optics are above the barrel does not matter for accuracy. If you need to turn the weapons sideways it is better if you have them closer to the barrel but that is something that is more likely you need to do with assault rifles than sniper rifles.

The main problem with a large offset is to avoid hitting something just in front of the barrel. If you are on the uneven ground something could be in front of the barrel but not in front of the sight. Lay down on the uneven ground and try to expose your body as little as possible to enemy fire then you risk just seeing over some dirt that is directly in front of the muzzle. This is the

Both are correct.

they are accurate because someone "zeroed" it in, or made it accurate. it is important to understand that that is only done at a specific range. for example, a rifle could be zeroed at one hundred yards, so if you want to hit something at that range, you would put the crosshair directly on it. if you want to hit something beyond that, you would need to use the stadia marks underneath the crosshair to aim above the impact point you want.

In real life, the scope doesn't line up perfectly. You "zero" a scope so that the bullet will hit on the crosshair at a certain distance, and at every other distance you adjust.

A real sniper will determine the range to the target, adjust for wind and other factors, and aim for a point some distance above and to the side of a target to account for the factors that will result in the bullet hitting away from the crosshair.

For example, you're shooting at a target 500m away. You know that at that distance your bullet will hit 3m below the target, and the wind will push the bullet .5m to the right in that time. So you aim 3m up and .5m to the left of where you want to the bullet to land.

A more complicated, related example is how WW2 fighter aircraft machine guns were aimed.

There might be, for example, four guns on each wing. The aiming reticle is in the cockpit, between them. The whole shebang is adjusted so that the bullets from each side converge (for example) one hundred meters ahead of the plane, and the aiming reticle points at that spot. This adjustment has to account for the angles from left and right, as well as the bullet drop, and air drag at a particular airspeed.

Like with the rifle scope, the pilot's aiming reticle has extra marks on it to allow aiming at other distances, and especially for leading a moving target.

Scopes intended for long ranges will typically have multiple markers for multiple ranges. I.e., along one long vertical line, you have a specific horizontal line for 100 yards, and another one for 200 yards, and another one for 300 yards, etc.

These account for basic bullet drop, but then you will have to do some on-the-fly adjustment for things like wind. This is one of the reasons why, in the military, someone in a "sniper" role often has a "spotter"... the recoil action of the rifle might throw the sniper's viewing window way off and require him to have to re-aim all over again the for next shot, but the spotter has an unaffected view of where the last shot landed to help the sniper recalculate the next shot.

Yep. This is especially observable in archery, since arrows drop off over such a shorter distance than bullets. With a simple bow and arrow, if you can hit something at 20 yards by aiming straight at it, then at 30 yards you'll have to aim quite a bit higher, and at 40 yards you'll have to aim much higher. The principle carries true to firearms, albeit over longer distances since the projectiles are traveling faster and thus travel further while under the same pull of gravity.