How does the focal length of an objective lens affect overall magnification in a telescope and a microscope?

What would happen to the overall magnifications of a telescope and a microscope if the focal lengths of their objective lenses are decreased?

The overall magnification of the telescope would decrease, and the overall magnification of the microscope would increase.

When the focal lengths of the objective lenses in a telescope and a microscope are decreased, the overall magnifications of both instruments are affected. In a telescope, the overall magnification is determined by the ratio of the focal length of the objective lens to the focal length of the eyepiece. If the focal length of the objective lens is decreased, the overall magnification will decrease because the ratio will be smaller.

On the other hand, in a microscope, the overall magnification is determined by the ratio of the focal length of the objective lens to the focal length of the eyepiece, multiplied by a factor for the tube length. If the focal length of the objective lens is decreased, the overall magnification will increase because the ratio will be larger.

Therefore, decreasing the focal lengths of the objective lenses will result in a decrease in the overall magnification of the telescope and an increase in the overall magnification of the microscope. It is important to note that the specific design and configuration of the instruments may play a role in the overall magnification, but the general principle remains the same.