Final answer:
In a compound microscope, using an objective lens b with double the focal length of lens a would result in half the magnification that lens a provides when all other factors remain constant.
Step-by-step explanation:
The question asks about the magnification obtained when using two different objective lenses with focal lengths fa and fb, where fb = 2fa, in a compound microscope. The magnification of a compound microscope is the product of the linear magnification of the objective and the angular magnification of the eyepiece. Given that the magnification obtained using lens a is Ma, it is implied that when lens b is used, which has a focal length double that of lens a, the magnification will be different due to the differences in the linear magnification produced by each objective lens.
As we know, the magnification of the objective is inversely proportional to its focal length; therefore, using the objective with focal length fb, being twice the focal length of objective a, would produce half the magnification of lens a (Mb = Ma/2) if no other factors were changed. However, the overall net magnification of the microscope, Mnet, also depends on the eyepiece used. Without changing the eyepiece, the final magnification would be half of what was obtained with lens a.