SATHEE: Optics 2 Question 23

Optics 2 Question 23

23. For two structures namely $S_{1}$ with $n_{1} = \frac{\sqrt{45}}{4}$ and $n_{2} = \frac{3}{2}$ , and $S_{2}$ with $n_{1} = \frac{8}{5}$ and $n_{2} = \frac{7}{5}$ and taking the refractive index of water to be $\frac{4}{3}$ and that to air to be 1 , the correct options is/are

(2015 Adv.)

(a) $N A$ of $S_{1}$ immersed in water is the same as that of $S_{2}$ immersed in a liquid of refractive index $\frac{16}{3 \sqrt{15}}$

(b) $N A$ of $S_{1}$ immersed in liquid of refractive index $\frac{6}{\sqrt{15}}$ is the same as that of $S_{2}$ immersed in water

(d) $N A$ of $S_{1}$ placed in air is the same as that of $S_{2}$ placed in water

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Answer:

Correct Answer: 23. $(a, c)$

Solution:

$\frac{4}{3} \sin i = \frac{\sqrt{45}}{4} \sin (90 - θ_{c}) = \frac{\sqrt{45}}{4} \cos θ_{c}$

$\sin θ_{c} = \frac{n_{2}}{n_{1}}$

$∴ \cos θ_{c} = \sqrt{1 - {\frac{n_{2}}{n_{1}}}^{2}}$

$\Rightarrow \frac{4}{3} \sin i = \frac{\sqrt{45}}{4} \frac{3}{\sqrt{45}}$

$\sin i = \frac{9}{16}$

In second case,

$\begin{array}{r} \sin θ_{c} = \frac{n_{2}}{n_{1}} = \frac{7}{8} \Rightarrow \cos θ_{c} = \frac{\sqrt{15}}{8} \\ \frac{16}{3 \sqrt{15}} \sin i = \frac{8}{5} \sin (90 - θ_{c}) \end{array}$

Simplifying we get,

$\sin i = \frac{9}{16}$

Same approach can be adopted for other options. Correct answers are (a) and (c).

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Optics 2 Question 23

23. For two structures namely $S_{1}$ with $n_{1} = \frac{\sqrt{45}}{4}$ and $n_{2} = \frac{3}{2}$ , and $S_{2}$ with $n_{1} = \frac{8}{5}$ and $n_{2} = \frac{7}{5}$ and taking the refractive index of water to be $\frac{4}{3}$ and that to air to be 1 , the correct options is/are

Answer:

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Optics 2 Question 23

23. For two structures namely S1 with n1=454 and n2=32, and S2 with n1=85 and n2=75 and taking the refractive index of water to be 43 and that to air to be 1 , the correct options is/are

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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23. For two structures namely $S_{1}$ with $n_{1} = \frac{\sqrt{45}}{4}$ and $n_{2} = \frac{3}{2}$ , and $S_{2}$ with $n_{1} = \frac{8}{5}$ and $n_{2} = \frac{7}{5}$ and taking the refractive index of water to be $\frac{4}{3}$ and that to air to be 1 , the correct options is/are