SATHEE: Optics 2 Question 24

Optics 2 Question 24

24. If two structures of same cross-sectional area, but different numerical apertures $N A_{1}$ and $N A_{2} (N A_{2} < N A_{1})$ are joined longitudinally, the numerical aperture of the combined structure is

(2015 Adv.)

(a) $\frac{N A_{1} N A_{2}}{N A_{1} + N A_{2}}$

(b) $N A_{1} + N A_{2}$

(d) $N A_{2}$

Integer Answer Type Question

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Answer:

Correct Answer: 24. (d)

Solution:

(1) $\sin i_{m} = n_{1} \sin (90^{\circ} - θ_{c})$

$\Rightarrow \sin i_{m} = n_{1} \cos θ_{c}$

$\Rightarrow N A = n_{1} \sqrt{1 - \sin^{2} θ_{c}}$

$= n_{1} \sqrt{1 - \frac{n_{2}^{2}}{n_{1}^{2}}} = \sqrt{n_{1}^{2} - n_{2}^{2}}$

Substituting the values we get,

$\begin{aligned} N A_{1} = \frac{3}{4} and N A_{2} = \frac{\sqrt{15}}{5} = \sqrt{\frac{3}{4}} \\ N A_{2} < N A_{1} \end{aligned}$

Therefore, the numerical aperture of combined structure is equal to the lesser of the two numerical aperture, which is $N A_{2}$ .

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Optics 2 Question 24

24. If two structures of same cross-sectional area, but different numerical apertures $N A_{1}$ and $N A_{2} (N A_{2} < N A_{1})$ are joined longitudinally, the numerical aperture of the combined structure is

Integer Answer Type Question

Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

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सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Optics 2 Question 24

24. If two structures of same cross-sectional area, but different numerical apertures NA1 and NA2(NA2<NA1) are joined longitudinally, the numerical aperture of the combined structure is

Integer Answer Type Question

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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24. If two structures of same cross-sectional area, but different numerical apertures $N A_{1}$ and $N A_{2} (N A_{2} < N A_{1})$ are joined longitudinally, the numerical aperture of the combined structure is