Simple question really. When you double the ISO does it mean your shutter speed needs to be half of the original value to have the same brightness in the image?
Assuming you want the same image brightness¹, if you increase the ISO setting by one stop and leave the aperture value the same, you need to reduce the exposure time by one stop.
Reducing exposure time by one stop can be described as:
- Halving exposure time (e.g. reducing exposure time from 1/250 second to 1/500 second)
- Doubling "shutter speed" (e.g. often referred to as increasing "shutter speed" from 1/250 to 1/500 - even though 1/250 is a larger number than 1/500)
The ambiguity of what "increasing" and "decreasing" shutter speed means is why I tend to avoid the term and use exposure time instead.
¹ The image projected by the lens onto the sensor will not be brighter or darker. At the same aperture it will be the same brightness regardless of the exposure time or the ISO setting. But the resulting photograph will vary in brightness based on how long the image is allowed to be projected onto the sensor and how much the collected light is then amplified. When either is halved and the other is doubled, if all other factors are equal the resulting photograph will have the same brightness.