SATHEE: Optics 4 Question 4

Optics 4 Question 4

4. A parallel beam of light is incident from air at an angle $α$ on the side $P Q$ of a right angled triangular prism of refractive index $n = \sqrt{2}$ . Light undergoes total internal reflection in the prism at the face $P R$ when $α$ has a minimum value of $45^{\circ}$ . The angle $θ$ of the prism is

(2016 Adv.)

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Answer:

Correct Answer: 4. (a)

Solution:

Applying Snell’s law at $M$ ,

$\begin{aligned} n & = \frac{\sin α}{\sin r_{1}} \Rightarrow \sqrt{2} = \frac{\sin 45^{\circ}}{\sin r_{1}} \\ \Rightarrow \sin r_{1} & = \frac{\sin 45^{\circ}}{\sqrt{2}} = \frac{1 / \sqrt{2}}{\sqrt{2}} = \frac{1}{2} \\ r_{1} & = 30^{\circ} \\ \sin θ_{c} & = \frac{1}{n} = \frac{1}{\sqrt{2}} \Rightarrow θ_{c} = 45^{\circ} \end{aligned}$

Let us take $r_{2} = θ_{c} = 45^{\circ}$ for just satisfying the condition of TIR.

In $△ P N M$ ,

$\begin{aligned} θ + 90 + r_{1} + 90 - r_{2} & = 180^{\circ} \\ o r θ = r_{2} - r_{1} = 45^{\circ} - 30^{\circ} & = 15^{\circ} \end{aligned}$

NOTE

If $α > 45^{\circ}$ (the given value). Then, $r_{1} > 30^{\circ}$ (the obtained value)

$∴ r_{2} - r_{1} = θ or r_{2} = θ + r_{1}$

or TIR will take place. So, for taking TIR under all conditions $α$ should be greater than $45^{\circ}$ or this is the minimum value of $α$ .

Optics 4 Question 4

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Optics 4 Question 4

4. A parallel beam of light is incident from air at an angle α on the side PQ of a right angled triangular prism of refractive index n=2. Light undergoes total internal reflection in the prism at the face PR when α has a minimum value of 45∘. The angle θ of the prism is

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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