For the same magnification, which telescope is typically longer?

For the same magnification, which telescope is typically longer?

• A. Keplerian
• B. Galilean
• C. Either
• D. None

Answer: (A)

When comparing telescopes at the same magnification, the overall length depends on the sign of the eyepiece’s focal length. In a Keplerian setup, both objective and eyepiece are positive focal length lenses, so the tube length adds: length = fo + fe. In a Galilean setup, the eyepiece has a negative focal length, so the length is the difference: length = fo − |fe|. For the same magnification m, the eyepiece focal length relates to the objective by fe ≈ fo/m in the Keplerian case. Then the Keplerian length is fo + fo/m = fo(1 + 1/m). In the Galilean case, the length is fo − fo/m = fo(1 − 1/m). With magnifications greater than 1, 1 + 1/m is greater than 1 − 1/m, so the Keplerian tube is longer. In short, the Keplerian telescope is typically longer for the same magnification because you add the eyepiece’s focal length, whereas the Galilean configuration effectively subtracts it.

When comparing telescopes at the same magnification, the overall length depends on the sign of the eyepiece’s focal length. In a Keplerian setup, both objective and eyepiece are positive focal length lenses, so the tube length adds: length = fo + fe. In a Galilean setup, the eyepiece has a negative focal length, so the length is the difference: length = fo − |fe|.

For the same magnification m, the eyepiece focal length relates to the objective by fe ≈ fo/m in the Keplerian case. Then the Keplerian length is fo + fo/m = fo(1 + 1/m). In the Galilean case, the length is fo − fo/m = fo(1 − 1/m). With magnifications greater than 1, 1 + 1/m is greater than 1 − 1/m, so the Keplerian tube is longer.

In short, the Keplerian telescope is typically longer for the same magnification because you add the eyepiece’s focal length, whereas the Galilean configuration effectively subtracts it.