SATHEE: Optics 4 Question 14

Optics 4 Question 14

14. A glass prism of refractive index 1.5 is immersed in water (refractive index 4/3). A light beam incident normally on the face $A B$ is totally reflected to reach the face $B C$ if

(1981, 3M)

(a) $\sin θ > 8 / 9$

(b) $2 / 3 < \sin θ < 8 / 9$

(d) None of these

Objective Question II (One or more correct option)

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Solution:

Let $θ_{c}$ be the critical angle at face $B C$ , then

Angle of incidence at face $B C$ is $i = θ$

Total internal reflection (TIR) will take place on this surface if, $i > θ_{c}$ or $θ > θ_{c}$ or $\sin θ > \sin θ_{c}$ or $\sin θ > \frac{8}{9}$

15 The minimum deviation produced by a prism

$\begin{aligned} δ_{m} & = 2 i - A = A \\ ∴ i_{1} & = i_{2} = A and \\ r_{1} & = r_{2} = A / 2 \\ ∴ r_{1} & = i_{1} / 2 \end{aligned}$

Now, using Snell’s law

$\sin A = μ \sin A / 2$

$\Rightarrow μ = 2 \cos (A / 2)$

For this prism when the emergent ray at the second surface is tangential to the surface

$\begin{aligned} i_{2} = π / 2 \Rightarrow r_{2} = θ_{c} \Rightarrow r_{1} = A - θ_{c} \\ so, \sin i_{1} = μ \sin (A - θ_{c}) \\ so, i_{1} = \sin^{- 1} \sin A \sqrt{4 \cos^{2} \frac{A}{2} - 1} - \cos A \end{aligned}$

For minimum deviation through isosceles prism, the ray inside the prism is parallel to the base of the prism if $∠ B = ∠ C$ .

But it is not necessarily parallel to the base if,

$∠ A = ∠ B or ∠ A = ∠ C$

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Optics 4 Question 14

14. A glass prism of refractive index 1.5 is immersed in water (refractive index 4/3). A light beam incident normally on the face $A B$ is totally reflected to reach the face $B C$ if

Objective Question II (One or more correct option)

Solution:

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 4 Question 14

14. A glass prism of refractive index 1.5 is immersed in water (refractive index 4/3). A light beam incident normally on the face AB is totally reflected to reach the face BC if

Objective Question II (One or more correct option)

Solution:

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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14. A glass prism of refractive index 1.5 is immersed in water (refractive index 4/3). A light beam incident normally on the face $A B$ is totally reflected to reach the face $B C$ if