An astronomical telescope has an angular magnification of
magnitude 5 for far objects. The separation between the
objective and the eyepiece is 36 cm and the final image is
formed at infinity. The focal length $f_o$ of the objective and
the focal length $f_e$ of the eyepiece are
- $f_o$= 45 cm and $f_e$= - 9 cm
- $f_o$= 50 cm and $f_e$= 10 cm
- $f_o$= 7.2 cm and $f_e$= 5 cm
- $f_o$= 30 cm and $f_e$= 6 cm
The Correct Option is D
Solution and Explanation
because objective is focussed for distant objects. Therefore,
$\hspace25mm P_1 I_1=f_o$
Further $I_1$ should lie at first focus of eyepiece because final
image is formed at infinity.
$\therefore \hspace25mm P_2 I_1=f_e$
Given $\hspace20mm P_1 P_2=$36 cm
$\therefore \hspace20mm f_o+f_e=36 \hspace25mm ...(i)$
Further angular magnification is given as 5. Therefore,
$\hspace25mm \frac{f_o}{f_e}=5 \hspace20mm ...(ii)$
Solving Eqs. (i) and (ii), we get
$\hspace15mm f_o=30$cm and $f_e=$6 cm
$\therefore$Correct option is (d).
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Concepts Used:
Optical instruments
A device that processes light waves (or photons), either to enhance an image for viewing or to analyze and determine its characteristic properties is called an optical instrument (or "optic" for short).
Applications of Optical Instruments:
- Microscope - It is one of the most extensively used optical instruments comprised of only one lens or combination of the lenses for magnifying and inspecting bodies that are too small to be seen in detail by clear eyes. Earlier microscopes had only one lens, and are, therefore, called simple microscopes, but the present microscopes are accessible with at least two lenses and thereby, termed a compound microscope.
- Telescope - It is another remarkable optical instrument. It makes distant objects emerge nearer by using an arrangement of lenses or lenses and curved mirrors that is used to observe the objects by absorption, emission, and reflection of their electromagnetic radiation to furnish a magnified image. As they are used to view objects that are far away, they include at least two lenses.