SATHEE: Optics 2 Question 3

Optics 2 Question 3

3. In figure, the optical fibre is $l = 2 m$ long and has a diameter of $d = 20 μ m$ . If a ray of light is incident on one end of the fibre at angle $θ_{1} = 40^{\circ}$ , the number of reflections it makes before emerging from the other end is close to (refractive index of fibre is 1.31 and $\sin 40^{\circ} = 0.64$ )

(Main 2019, 8 April I)

(a) 55000

(b) 66000

(d) 57000

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Answer:

Correct Answer: 3. (d)

Solution:

Total internal reflection occurs through given glass rod as shown in figure.

From Snell’s law, $n_{1} \sin i = n_{2} \sin r$

where, $n_{1} = 1, n_{2} = 1.31$ and $i = 40^{\circ}$

So, we get

$1 \sin 40^{\circ} = 1.31 \sin r \Rightarrow \sin r = \frac{0.64}{1.31} = 0.49 \approx 0.5$

So, $r = 30^{\circ}$

From $△ O A B, θ = 90 - r = 60^{\circ}$

Now, $\tan θ = \frac{x}{20 μ m}$

$\Rightarrow x = 20 \sqrt{3} μ m [∵ \tan 60^{\circ} = \sqrt{3}]$

One reflection occurs in $20 \sqrt{3} μ m$ .

$∴$ Total number of reflections occurring in $2 m$

$\begin{aligned} = n = \frac{2 m}{20 \sqrt{3} μ m} = \frac{2}{20 \sqrt{3} \times 10^{- 6}} \\ = 57735 reflections \approx 57000 reflections \end{aligned}$

Optics 2 Question 3

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Optics 2 Question 3

3. In figure, the optical fibre is l=2m long and has a diameter of d=20μm. If a ray of light is incident on one end of the fibre at angle θ1=40∘, the number of reflections it makes before emerging from the other end is close to (refractive index of fibre is 1.31 and sin⁡40∘=0.64 )

Answer:

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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