SATHEE: Optics 1 Question 4

Optics 1 Question 4

4. The plane mirrors $(M_{1}$ and $M_{2})$ are inclined to each other such that a ray of light incident on mirror $M_{1}$ and parallel to the mirror $M_{2}$ is reflected from mirror $M_{2}$ parallel to the mirror $M_{1}$ . The angle between the two mirror is

(2019 Main, 9 Jan II)

(a) $45^{\circ}$

(b) $75^{\circ}$

(d) $60^{\circ}$

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Answer:

Correct Answer: 4. (d)

Solution:

The given condition is shown in the figure given below, where two plane mirror inclined to each other such that a ray of light incident on the first mirror $(M_{1})$ and parallel to the second mirror $(M_{2})$ is finally reflected from second mirror ( $M_{2}$ ) parallel to the first mirror.

where, $P Q =$ incident ray parallel to the $mirror M_{2}$ , $Q R =$ reflected ray from the mirror $M_{1}$ , $R S =$ reflected ray from the mirror $M_{2}$ which is parallel to the $M_{1}$ and $θ = angle$ between $M_{1}$ and $M_{2}$ .

According to geometry,

$∠ P A S = ∠ P Q M_{1} = θ ($ angle on same line $)$

$∠ A Q N_{1} =$ angle of incident $= 90 - θ$

$∠ N_{1} Q R =$ angle of reflection $= (90 - θ)$ .

Therefore, for triangle $△ O R Q$ , (according to geometry)

$\begin{matrix} ∠ θ + ∠ θ + ∠ O R Q = 180^{\circ} \\ ∠ O R Q = 180^{\circ} - 2 θ \end{matrix}$

For normal $N_{2}$ ,

angle of incident $=$ angle of reflection

$= 2 θ - 90^{\circ}$

Therefore, for the triangle $△ R A Q$

$\begin{aligned} \Rightarrow 4 θ - 180^{\circ} + 180^{\circ} - 2 θ + θ & = 180 \\ 3 θ = 180^{\circ} \Rightarrow θ & = 60^{\circ} \end{aligned}$

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Optics 1 Question 4

4. The plane mirrors $(M_{1}$ and $M_{2})$ are inclined to each other such that a ray of light incident on mirror $M_{1}$ and parallel to the mirror $M_{2}$ is reflected from mirror $M_{2}$ parallel to the mirror $M_{1}$ . The angle between the two mirror is

Answer:

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Optics 1 Question 4

4. The plane mirrors (M1 and M2) are inclined to each other such that a ray of light incident on mirror M1 and parallel to the mirror M2 is reflected from mirror M2 parallel to the mirror M1. The angle between the two mirror is

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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4. The plane mirrors $(M_{1}$ and $M_{2})$ are inclined to each other such that a ray of light incident on mirror $M_{1}$ and parallel to the mirror $M_{2}$ is reflected from mirror $M_{2}$ parallel to the mirror $M_{1}$ . The angle between the two mirror is