SATHEE: Optics 2 Question 31

Optics 2 Question 31

30. A right angled prism is to be made by selecting a proper material and the angles $A$ and $B (B \leq A)$ , as shown in figure. It is desired that a ray of light incident on the face $A B$ emerges parallel to the incident direction after two internal reflections.

(1987, 7M)

(a) What should be the minimum refractive index $n$ for this to be possible?

(b) For $n = 5 / 3$ is it possible to achieve this with the angle $B$ equal to 30 degrees?

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Answer:

Correct Answer: 30. (a) $\sqrt{2}$

(b) No

Solution:

(a) At $P$ , angle of incidence $i_{A} = A$ and at $Q$ , angle of incidence $i_{B} = B$

If TIR satisfies for the smaller angle of incidence than for larger angle of incidence is automatically satisfied.

$B \leq A ∴ i_{B} \leq i_{A}$

Maximum value of $B$ can be $45^{\circ}$ . Therefore, if condition of TIR is satisfied, then condition of TIR will be satisfied for all value of $i_{A}$ and $i_{B}$

$\begin{aligned} Thus, & 45^{\circ} & \geq θ_{c} \\ or & \sin 45^{\circ} & \geq \sin θ_{c} \\ or & \frac{1}{\sqrt{2}} & \geq \frac{1}{μ} or μ \geq \sqrt{2} \end{aligned}$

$∴$ Minimum value of $μ$ or $n$ is $\sqrt{2}$ .

(b) For $n = \frac{5}{3}, \sin θ_{c} = \frac{1}{n} = \sin^{- 1} \frac{3}{5} \approx 37^{\circ}$

If $B = 30^{\circ}$ , then $i_{B} = 30^{\circ}$

then $A = 60^{\circ}$ or $i_{A} = 60^{\circ}$

$i_{A} > θ_{c}$ but $i_{B} < θ_{c}$

i.e. TIR will take place at $A$ but not at $B$ .

or we write : $\sin i_{B} < \sin θ_{c} < \sin i_{A}$

$\sin 30^{\circ} < \frac{3}{5} < \sin 60^{\circ}$

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Optics 2 Question 31

30. A right angled prism is to be made by selecting a proper material and the angles $A$ and $B (B \leq A)$ , as shown in figure. It is desired that a ray of light incident on the face $A B$ emerges parallel to the incident direction after two internal reflections.

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

Optics 2 Question 31

30. A right angled prism is to be made by selecting a proper material and the angles A and B(B≤A), as shown in figure. It is desired that a ray of light incident on the face AB emerges parallel to the incident direction after two internal reflections.

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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30. A right angled prism is to be made by selecting a proper material and the angles $A$ and $B (B \leq A)$ , as shown in figure. It is desired that a ray of light incident on the face $A B$ emerges parallel to the incident direction after two internal reflections.