Someone with ‘normal’ 20/20 or 6/6 vision (visual acuity) is just able to decipher a letter (eg. E) that subtends a visual angle of 5 minutes of arc (5') at the eye. What this means is that if you draw a line from the top of a 20/20 letter (E) to the eye and another line from the bottom of the letter to the eye, the size of the angle at the intersection of these two lines at the eye is 5' of arc. It does not matter how far away something is from the eye, as long as it subtends an angle of 5' of arc at the eye, then a person with 20/20 visual acuity will just be able to distinguish what it is.
For shooting range up to 1000 metres, the bullet diameter is assumed to be about 0.45” or 11.43mm. If we know how far an individual with 20/20 vision can see an 11.43mm bullet hole with naked eye, we can then work out how many times the same target should be brought closer from 1000 metres (i.e., times of magnification).
Here is a calculation on how far one can see this 11.43mm target, where:
The simple trigonometry is calculated as:
(1). 2.5’ of arc / 60=0.04167 degrees
(2). Tangent 0.04167 degrees=h/d=5.72mm/d (note: 11.43/2=5.72)
This means that an individual with normal vision will be able to read a letter with 11.43mm height (i.e., to identify the direction of letter E) at about 8 metres. In fact, to see a round bullet hole is much easier than reading a letter. A field test has indicated that an 11mm white dot on black background (or black on white) can be seen by people with normal vision at 10m or slightly further. In other words, if the same target is placed 1000m away, it needs to be magnified (or 'brought closer') 1000/10=100 times.
For the Nipon 350x70 scope, with the K9mm eyepiece and 3x Barlow lens included, it can achieve a 120x magnification which is within the power required for this purpose.
If a target is located at 150 yards (140m), with a 0.22” (5.69mm) bullet, the required scope magnification can be calculated as: 140÷(5.69÷2÷0.00072÷1000)=35x
It needs to be understood that magnification is only one basic aspect which needs to be considered in this example. There are other factors that also play important role in target observation, such as the size of the objective lens and optical coatings of the scope, which affect image clarity.