ray-optics-and-optical-instruments Question 44
Question: Q. 2. (i) Draw a labelled ray diagram of an astronomical telescope to show the image formation of a distant object. Write the main considerations required in selecting the objective and eyepiece lenses in order to have large magnifying power and high resolution of the telescope.
(ii) A compound microscope has an objective of focal length $1.25 \mathrm{~cm}$ and eyepiece of focal length $5 \mathrm{~cm}$. A small object is kept at $2.5 \mathrm{~cm}$ from the objective. If the final image formed is at infinity, find the distance between the objective and the eyepiece.
U] [Foreign 2014]
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Solution:
Ans. (i) Try yourself, Similar to Q. 1, Short Answer Type Questions-II
Alternatively,
For a large magnifying power, $f_{\mathrm{o}}$ should be large and $f_{e}$ should be small.
For a higher resolution, the diameter of the objective should be large.
$$ \begin{align*} & \frac{1}{v_{0}}-\frac{1}{u_{0}}=\frac{1}{f_{0}} \tag{ii}\ & \frac{1}{v_{0}}=\frac{1}{f_{0}}+\frac{1}{u_{0}}=\frac{1}{1.25}-\frac{1}{2.5}=\frac{1}{-2.5} \ & v_{\mathrm{o}}=-2.5 \mathrm{~cm} \ & L=\left|f_{0}\right|+\left|f_{e}\right| \ &=(2.5+5.0) \mathrm{cm}=7.5 \mathrm{~cm} \quad 1 / 2 \ & 1 / 2 \end{align*} $$
[Note for students : You may draw refractive or reflective telescope].
[CBSE Marking Scheme 2014]
