When should the high power objective used?

A higher power objective lens in a microscope is used when greater magnification is needed to study an object.

The higher power objective lens has a shorter focal length and needs to be closer to the object being studied. It has a smaller aperture (lens diameter) so it has a narrower field of vision and may require more light to be useful. This means that it is more difficult to find and center the item being studied under the lens and it is harder to focus the lens on the object.