The magnifying power of a telescope is given as 9, with the distance between the objective and eyepiece being 20 cm when adjusted for parallel rays. We need to find the ratio of the focal length of the objective lens to the focal length of the eyepiece, denoted as
m.
To determine this ratio:
Magnifying Power Formula:
The magnifying power of a telescope
m is defined by the formula:
m=‌where
f0 is the focal length of the objective lens and
fe is the focal length of the eyepiece lens.
Given Values:
m=9⇒‌=9Thus, we can express the focal length of the objective lens as:
f0=9feDistance Between Lenses:
The total distance between the objective and eyepiece is given by:
f0+fe=20‌cmSubstitute and Solve:
Substitute the expression for
f0 into the distance equation:
‌9fe+fe=20‌10fe=20Solving this gives:
fe=2‌cmFinding
f0 :
Using the relationship between
f0 and
fe :
f0=9×2=18‌cmRatio Calculation:
The ratio of the focal lengths is:
‌=‌=9Therefore, the value of
m is 9 .