Whether or not your spotter will be able to clearly see or resolve a bullet hole in a distant target depends on the size of the bullet, the size of hole it makes and the range to the target. These numbers are used to calculate the angular size of the bullet hole. Then you can compare the angular size to the resolving power of your scope to see if it’s adequate.
First, we’ll assume the bullet hole is the same size as the bullet. The holes are often larger, so this is a conservative assumption.
If necessary, convert hole size and range to inches.
To calculate the angular size of the bullet hole, divide the size of the bullet hole by the range. Multiply the result by 206,265. The number you get will be the angular size in arc-seconds of the hole as seen from the shooting line.
Compare this number to the following chart to find out which scope is best for your target spotting.
Example: a 50-caliber bullet hole in a target at 1000 yards. What size scope is the smallest I can use to spot this hole?
1000 yards equals 1000x3x12 or 36,000 inches. 0.50 divided by 36000 is 0.0000138.
0.0000138 x 206265 = 2.8 arc-seconds
A 65mm scope will clearly resolve 2.8 arc-seconds. So you would need at least a 65mm objective size spotting scope to see your shot.
Other factors affecting your ability to see the bullet hole are air quality, steadiness of the air and lighting conditions.