SATHEE: Optics Question 462

Optics Question 462

Question: In the adjacent diagram, CP represents a wave front and AO and BP, the corresponding two rays. Find the condition on $θ$ for constructive interference at P between the ray BP and reflected ray OP

Options:

A) $\cos θ = 3 λ / 2 d$

B) $\cos θ = λ / 4 d$

C) $\sec θ - \cos θ = λ / d$

D) $\sec θ - \cos θ = 4 λ / d$

Show Answer

Answer:

Correct Answer: B

Solution:

[b]

$∴ P R = d \Rightarrow P O = d \sec θ$

and $C O = P O \cos 2 θ = d \sec θ \cos 2 θ$ is Path difference between the two rays $Δ = C O + P O$

$= (d \sec θ + d \sec θ \cos 2 θ)$

Phase difference between the two rays is $ϕ = π$ (One is reflected, while another is direct)

Therefore condition for constructive interference should be $Δ = \frac{λ}{2}, \frac{3 λ}{2}, \dots$

Or $d \sec θ (1 + c o s 2 θ) = \frac{λ}{2}$

Or $\frac{d}{\cos θ} (2 c o s^{2} θ) = \frac{λ}{2} \Rightarrow \cos θ = \frac{λ}{4 d}$

Optics Question 462

Question: In the adjacent diagram, CP represents a wave front and AO and BP, the corresponding two rays. Find the condition on $θ$ for constructive interference at P between the ray BP and reflected ray OP

Options:

Answer:

Solution:

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Optics Question 462

Question: In the adjacent diagram, CP represents a wave front and AO and BP, the corresponding two rays. Find the condition on θ for constructive interference at P between the ray BP and reflected ray OP

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: In the adjacent diagram, CP represents a wave front and AO and BP, the corresponding two rays. Find the condition on $θ$ for constructive interference at P between the ray BP and reflected ray OP