BITSAT 2024 Shift 1 Paper

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=‌

f0

fe

where f0 is the focal length of the objective lens and fe is the focal length of the eyepiece lens.
Given Values:
m=9⇒‌

f0

fe

=9
Thus, we can express the focal length of the objective lens as:
f0=9fe
Distance Between Lenses:
The total distance between the objective and eyepiece is given by:
f0+fe=20‌cm
Substitute and Solve:

Substitute the expression for f0 into the distance equation:
‌9fe+fe=20
‌10fe=20
Solving this gives:
fe=2‌cm
Finding f0 :
Using the relationship between f0 and fe :
f0=9×2=18‌cm
Ratio Calculation:
The ratio of the focal lengths is:
‌

f0

fe

=‌

18

2

=9
Therefore, the value of m is 9 .