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.