SATHEE: Optics 3 Question 36

Optics 3 Question 36

36. A thin plano-convex lens of focal length $f$ is split into two halves. One of the halves is shifted along the optical axis. The separation between object and image planes is $1.8 m$ . The magnification of the image formed by one of the half

lens is 2. Find the focal length of the lens and separation between the halves. Draw the ray diagram for image formation.

$(1996, 5$ M)

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Answer:

Correct Answer: 36. $0.4 m, 0.6 m$ 37. See the hints

Solution:

For both the halves, position of object and image is same. Only difference is of magnification. Magnification for one of the halves is given as $2 (> 1)$ . This can be for the first one, because for this, $| v | > | u |$ . Therefore, magnification, $| m | = | v / u | > 1$ . So, for the first half

$| v / u | = 2 or | v | = 2 | u |$

Let $u = - x$ then $v = + 2 x$ and $| u | + | v | = 1.8 m$

i.e. $3 x = 1.8 m$ or $x = 0.6 m$

Hence, $u = - 0.6 m$ and $v = + 1.2 m$ .

Using, $\frac{1}{f} = \frac{1}{v} - \frac{1}{u} = \frac{1}{1.2} - \frac{1}{- 0.6} = \frac{1}{0.4}$

$∴ f = 0.4 m$

For the second half

$\begin{aligned} \frac{1}{f} & = \frac{1}{1.2 - d} - \frac{1}{- (0.6 + d)} \\ \frac{1}{0.4} & = \frac{1}{1.2 - d} + \frac{1}{0.6 + d} \end{aligned}$

Solving this, we get $d = 0.6 m$ .

Magnification for the second half will be

$m_{2} = \frac{v}{u} = \frac{0.6}{- (1.2)} = - \frac{1}{2}$

and magnification for the first half is

$m_{1} = \frac{v}{u} = \frac{1.2}{- (0.6)} = - 2$

The ray diagram is as follows :

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Optics 3 Question 36

36. A thin plano-convex lens of focal length $f$ is split into two halves. One of the halves is shifted along the optical axis. The separation between object and image planes is $1.8 m$ . The magnification of the image formed by one of the half

Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

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अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

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Optics 3 Question 36

36. A thin plano-convex lens of focal length f is split into two halves. One of the halves is shifted along the optical axis. The separation between object and image planes is 1.8m. The magnification of the image formed by one of the half

Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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36. A thin plano-convex lens of focal length $f$ is split into two halves. One of the halves is shifted along the optical axis. The separation between object and image planes is $1.8 m$ . The magnification of the image formed by one of the half