A telescope has an objective with a refractive power of 1.65 diopters and an eyepiece with a refractive power of 240 diopters. What is the angular magnification of the telescope?
I keep getting 145.45
To find the angular magnification of a telescope, we need to use the formula:
Angular Magnification = (Theta prime) / (Theta)
Where:
- (Theta prime) is the angle subtended by the image formed by the eyepiece at the eye.
- (Theta) is the angle subtended by the object at the objective lens.
In this case, we are not given the values of (Theta prime) or (Theta). However, we can use the refractive powers of the lens to find these values.
The equation relating refractive power (P) and angle (Theta) is:
P = 1 / f
Where:
- P is the refractive power in diopters.
- f is the focal length in meters.
To find (Theta prime) and (Theta), we can use the refractive power and the formula P = 1 / f.
For the objective lens:
P1 = 1.65 diopters
(1.65 diopters) = 1 / f1
f1 = 1 / 1.65 = 0.606 meters
For the eyepiece:
P2 = 240 diopters
(240 diopters) = 1 / f2
f2 = 1 / 240 = 0.00417 meters
Now that we have the focal lengths, we can find the angles (Theta prime) and (Theta) using the formula:
(Theta prime) = (Object distance) / (f2)
(Theta) = (Object distance) / (f1)
Since the object distance is the same for both angles, we can cancel it out:
(Theta prime) / (Theta) = (f1) / (f2)
(Theta prime) / (Theta) = (0.606) / (0.00417)
Now we can calculate the angular magnification:
Angular Magnification = (Theta prime) / (Theta) = (0.606) / (0.00417) ≈ 145.85
Therefore, the angular magnification of the telescope is approximately 145.85.