SATHEE: ray-optics-and-optical-instruments Question 47

ray-optics-and-optical-instruments Question 47

Question: Q. 7. How is the working of a telescope different from that of a microscope? The focal lengths of the objective and eyepiece of a microscope are $1.25 cm$ and $5 cm$ respectively. Find the position of the object relative to the objective lens in order to obtain an angular magnification of 30 in normal adjustment. U] [Delhi I, II, III 2012]

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Solution:

Ans. Working differences :

(i) The objective of a telescope forms the image of a very far off object at, or within, the focus of its eyepiece. The microscope does the same for a small object kept just beyond the focus of its objective.

(ii) The final image formed by a telescope is magnified relative to its size as seen by the unaided eye, while the final image formed by a microscope is magnified relative to its absolute size.

(iii) The objective of a telescope has large focal length and large aperture, while the corresponding for a microscope have very small values.

Given : $f_{o} = 1.25 cm, f_{e} = 5 cm$

Angular magnification, $m = 30$

Now,

$m = m_{e} \times m_{o}$

In normal adjustment, the angular magnification of an eyepiece

$m_{e} = \frac{d}{f_{e}} = \frac{25}{5} = 5$

$m_{0} = 6$

$m_{0} = \frac{v_{0}}{u_{0}} \Rightarrow - 6 = \frac{v_{0}}{u_{0}}$

$v_{o} = - 6 u_{o}$

Applying lens equation to the objective lens :

$\begin{aligned} \frac{1}{f_{0}} & = \frac{1}{v_{0}} - \frac{1}{u_{0}} \frac{1}{1.25} & = \frac{1}{- 6 u_{0}} - \frac{1}{u_{0}} \frac{1}{1.25} & = \frac{- 1 - 6}{6 u_{0}} 6 u_{o} & = - 1.25 \times 7 u_{0} & = \frac{- 1.25 \times 7}{6} cm \end{aligned}$

$| u_{o} | = 1.46 cm$

[CBSE Marking Scheme 2012]

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Ray Optics And Optical Instruments

ray-optics-and-optical-instruments Question 47

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Ray Optics And Optical Instruments

ray-optics-and-optical-instruments Question 47

OSWAAL LEARNING TOOLS

For Suggested Online Videos

CHAPTER 10

Table of Contents

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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