exposure - How do I know which combination of aperture and shutter speed yields enough light to have pictures with minimal noise?

This is a kind of continuation of this question.

I'm shooting a poorly lit object. Camera has fastest ISO value of 3200. I set aperture to some specific value and don't alter it, the object is unchanged and the camera stands still. I first shoot with ISO 1600 and 1/125 second shutter speed, then with ISO 3200 and 1/250 second shutter speed. Pictures taken with ISO 1600 turn out rather clean and pictures with ISO 3200 turn out rather noisy. Both images look identically exposed.

The reason is with 1/250 second shutter speed lower amount of light enters the camera and higher ISO value causes more amplification of the signal and also more amplification of the noise and so more noise gets into the resulting image. With 1/125 second shutter speed twice as much light enters the camera and so less amplification is required and so noise is also amplified less and this causes less noise in the resulting image.

So I'm shooting a specific scene with a specific camera and all settings are left constant and I only vary either:

• the aperture and ISO value or


• the shutter speed and ISO value

so basically I vary the amount of light and the ISO value.

How do I know which amount of light (and so aperture or shutter speed) is the minimum required to obtain an image with low noise? How would I know without making the test shots that I need 1/125 shutter speed or slower?