The focal length of the objective of a telescope is 0.2 m and the eyepiece has a focal length of 1.6 m. What is the length of the telescope?
A. 1.8 m
B. 1.4 m
C. 1.6 m
D. .90 m
E. 8.0 m
The length of the telescope is 0.2 + 1.6
To find the length of the telescope, we can use the formula for the total magnification of a telescope:
Total magnification (M) = (-focal length of the objective) / (-focal length of the eyepiece)
We are given that the focal length of the objective (f1) is 0.2 m and the focal length of the eyepiece (f2) is 1.6 m.
Plugging in these values:
M = (-0.2 m) / (-1.6 m)
Now, we can simplify this expression:
M = 0.2 m / 1.6 m
To divide by fractions, we can multiply by the reciprocal of the divisor:
M = 0.2 m * (1 / 1.6 m)
M = 0.2 / 1.6
Now we can compute the value of M:
M = 0.125
The total magnification is 0.125.
The length of the telescope (L) can be calculated using the formula:
L = (focal length of the objective) + (focal length of the eyepiece) - (focal length of the objective) * (focal length of the eyepiece) / ((focal length of the objective) + (focal length of the eyepiece))
Plugging in the given values:
L = 0.2 m + 1.6 m - (0.2 m * 1.6 m) / (0.2 m + 1.6 m)
L = 1.8 m - (0.32 m^2) / 1.8 m
Now, we can calculate L:
L = 1.8 m - 0.32 m^2 / 1.8 m
L = 1.8 m - 0.18 m
L = 1.62 m
Therefore, the length of the telescope is approximately 1.62 m.
The correct answer is none of the options provided.