The focal length of objective of a telescope is 0.2 m and the eyepiece has a focal length of 1.6 m. What is the length of this telescope?
A) 8.0 m B) 1.4 m C) 1.6 m D) 1.8 m
Recheck you numbers. Telescopes have long focal lengths and their eyepieces (if used) have short focal lengths.
The telescope length, if you are using a refractor, is the sum of the objective and eyepiece focal lengths.
Assuming you got the numbers mixed up, the answer is 1.8 m
To find the length of the telescope, we need to use the formula:
1/f_total = 1/f_objective + 1/f_eyepiece
where f_total is the total focal length of the telescope, f_objective is the focal length of the objective lens, and f_eyepiece is the focal length of the eyepiece.
Given that the focal length of the objective lens is 0.2 m and the focal length of the eyepiece is 1.6 m, we can substitute these values into the formula:
1/f_total = 1/0.2 + 1/1.6
Simplifying the equation:
1/f_total = 5 + 0.625
1/f_total = 5.625
Now, we can find the reciprocal of both sides to solve for f_total:
f_total = 1 / (1/f_total)
f_total = 1 / 5.625
f_total = 0.1778 m
Therefore, the length of the telescope is approximately 0.1778 meters, which is equivalent to 1.8 meters.
So, the correct answer is option D) 1.8 m.