Question

The focal lengths of objective lens and eye lens of a Galilean Telescope are respectively $30cm$ and $3.0cm$. Telescopes produce virtual, erect images of an object situated far away from it at least distance of distinct vision from the eye lens. In this condition, the Magnifying Power of the Galilean Telescope should be:
(A) $+ 11.2$
(B) $- 11.2$
(C) $- 8.8$
(D) $+ 8.8$

Answer 1

Hint
To solve this question, we need to use the formula for the magnifying power of a Galilean Telescope. The parameters of the telescope are given in the question. Putting these in the expression of the magnifying power, we will easily get the final answer.
Formula Used: The formula used in solving this question is given by
$\Rightarrow m = \dfrac{{{f_0}}}{{{f_e}}}\left( {1 - \dfrac{{{f_e}}}{D}} \right)$
Here $m$ is the magnifying power of a Galilean Telescope, ${f_0}$ is the focal length of the objective lens, ${f_e}$ is the focal length of the eye lens, and $D$ is the least distance for the distinct vision for a human eye.

Complete step by step answer
We know that the magnifying power of a Galilean Telescope is given by
$\Rightarrow m = \dfrac{{{f_0}}}{{{f_e}}}\left( {1 - \dfrac{{{f_e}}}{D}} \right)$ … (1)
According to the question, we have the focal length of the objective lens, ${f_0} = 30cm$, and the focal length of the eye lens, ${f_e} = 3.0cm$ for the given Galilean Telescope.
Also, we know that the least distance for the distinct vision for the human eye is $D = 25cm$.
Putting these values in (1), we get
$\Rightarrow m = \dfrac{{30}}{3}\left( {1 - \dfrac{3}{{25}}} \right)$
On solving we get
$\Rightarrow m = + 8.8$
Thus the magnifying power of the given Galilean Telescope is equal to $+ 8.8$.
Hence, the correct answer is option D.

Note
We do not need to worry about the sign convention while putting the values of the focal lengths in the expression of the magnifying power of the Galilean Telescope. This is because the formula for the magnifying power has been derived taking care of all the sign conventions. So, simply the magnitudes of all the parameters must be substituted in this expression.