Q.What are the limitations in increasing the magnifying powers of

[!TLDR] All three instruments are limited by practical bounds on focal length/aperture: a simple microscope by lens thickness/aberration at very small f, a compound microscope by allowed tube length limiting mo, and a telescope by how large an objective can physically be built. [!ANSWER] Simple microscope: very small f (needed for high M) makes the lens thick, worsening spherical/chromatic aberration. Compound microscope: rai …

SIMPLE MICROSCOPE: since M_max=1+D/f and M_min=D/f, higher magnifying power requires a SMALLER focal length f. But a very small f forces the lens to be made thicker (more strongly curved) relative to its aperture, and a thick lens suffers markedly WORSE spherical aberration and chromatic aberration -- so in practice a simple microscope's usable magnifying power is capped by how small an f can be used before image quality degrades unacceptably, not by any formula limit.

COMPOUND MICROSCOPE: the overall power M=m_o x M_e can, in principle, be raised further by increasing m_o=v_o/u_o (pushing the object closer to the objective's focus). But doing so simultaneously increases v_o (the objective's own image distance), and since the instrument's overall length is L=v_o+u_e, a larger v_o directly means a LONGER instrument. So m_o -- and hence the overall M -- is fundamentally limited by how long the microscope tube is practically allowed to be; beyond some point, further magnification would require an impractically long (unwieldy, mechanically unstable) instrument. …

Address each of the three instruments in turn, identifying the SPECIFIC physical/practical constraint (aberration from a too-small f; tube length from a too-large vo; objective size/weight fr …

Giving one generic answer ('cannot be increased indefinitely') for all three instruments instead of identifying the distin …