SATHEE: Optics Question 127

Optics Question 127

Question: An optical fibre consists of core of m1 surrounded by a cladding of m2 < m1. A beam of light enters from air at an angle a with axis of fibre. The highest a for which ray can be travelled through fibre is

Options:

A) $\cos^{- 1} \sqrt{μ_{2}^{2} - μ_{1}^{2}}$

B) $\sin^{- 1} \sqrt{μ_{1}^{2} - μ_{2}^{2}}$

C) $\tan^{- 1} \sqrt{μ_{1}^{2} - μ_{2}^{2}}$

D) $\sec^{- 1} \sqrt{μ_{1}^{2} - μ_{2}^{2}}$

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Answer:

Correct Answer: B

Solution:

Here the requirement is that $i > c$

$\Rightarrow \sin i > \sin c \Rightarrow \sin i > \frac{μ_{2}}{μ_{1}}$ …(i) From Snell’s law $μ_{1} = \frac{\sin α}{\sin r}$ ..(ii) Also in $Δ O B A$

$r + i = 90^{o}$

$\Rightarrow r = (90 - i)$ Hence from equation (ii) $\sin α = μ_{1} \sin (90 - i)$

$\Rightarrow \cos i = \frac{\sin α}{μ_{1}}$

$\sin i = \sqrt{1 - \cos^{2} i}$

$= \sqrt{1 - {(\frac{\sin α}{μ_{1}})}^{2}}$ ..(iii) From equation (i) and (iii) $\sqrt{1 - {(\frac{\sin α}{μ_{1}})}^{2}} > \frac{μ_{2}}{μ_{1}}$

Therefore $\sin^{2} α < (μ_{1}^{2} - μ_{2}^{2})$

Therefore $\sin α < \sqrt{μ_{1}^{2} - μ_{2}^{2}}$

$α_{max} = \sin^{- 1} \sqrt{μ_{1}^{2} - μ_{2}^{2}}$

Optics Question 127

Question: An optical fibre consists of core of m1 surrounded by a cladding of m2 < m1. A beam of light enters from air at an angle a with axis of fibre. The highest a for which ray can be travelled through fibre is

Options:

Answer:

Solution:

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Optics Question 127

Question: An optical fibre consists of core of m­1 surrounded by a cladding of m2 < m1. A beam of light enters from air at an angle a with axis of fibre. The highest a for which ray can be travelled through fibre is

Options:

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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Question: An optical fibre consists of core of m1 surrounded by a cladding of m2 < m1. A beam of light enters from air at an angle a with axis of fibre. The highest a for which ray can be travelled through fibre is