Question

The eyepiece of a refracting telescope has a focal length of 9.58 cm. The distance between the objective and eyepiece is 1.80 m, and the final image is at infinity. What is the magnification of the telescope?

1) 1.80
2) 9.58
3) 1.80/9.58
4) 9.58/1.80

Answer 1

The magnification of a telescope is calculated as the focal length of the objective divided by that of the eyepiece. In this case, converting meters to centimeters for consistency, we get a magnification of approximately 18.79, indicating that option 4 (9.58/1.80) is incorrect.

Step-by-step explanation:

The magnification of a telescope is calculated by dividing the focal length of the objective (fo) by the focal length of the eyepiece (fe). Given that the eyepiece has a focal length of 9.58 cm and the final image is at infinity, we use a basic formula for magnification in telescopes, which is M = fo/fe. The distance between the objective and the eyepiece (1.80 m or 180 cm) in this case effectively serves as the focal length of the objective since the final image forms at infinity. Therefore, the magnification (M) of the telescope is:

M = fo/fe = 180 cm / 9.58 cm = 18.79 (approximately).

That said, none of the options provided is correct, and we must be careful to consider our units, as we have to first convert 1.80 m to cm to be consistent with the eyepiece's focal length in cm.