SATHEE: Optics Question 848

Optics Question 848

Question: In an interference arrangement similar to Young’s double-slit experiment, the slits $S_{1}$ and $S_{2}$ are illuminated with coherent microwave sources, each of frequency 106 Hz. The sources are synchronized to have zero phase difference. The slits are separated by a distance d = 150.0 m. The intensity I $(θ)$ is measured as a function of $θ$ , where $θ$ is defined as shown. If $I_{0}$ is the maximum intensity, then I $(θ)$ for is given by

Options:

A) $I (θ) = I_{0} / 2$ for $θ = 30^{o}$

B) $I (θ) = I_{0} / 4$ for $θ = 90^{o}$

C) $I (θ) = I_{0}$ for $θ = 0^{o}$

D) $I = θ$ is constant for all values of $θ$

Show Answer

Answer:

Correct Answer: C

Solution:

[c] We know that $I (θ) = I_{0} \cos^{2} \frac{δ}{2}$

where $δ = \frac{2 π d \tan θ}{λ}$

$I (θ) = I_{0} \cos^{2} (\frac{π d \tan θ}{π}) = I_{0} \cos^{2} (\frac{π \times 150 \times \tan θ}{3 \times 10^{8} / 10^{6}})$

$= I_{0} \cos^{2} (\frac{π}{2} \tan θ)$

For $θ = 30^{o}$ ; $I (θ) = I_{o} \cos^{2} (\frac{π}{2 \sqrt{3}})$ For $θ = 90^{o}$ ; $I (θ) = I_{o} \cos^{2} (\infty)$ For $θ = 0^{o}$

$I (θ) = I_{0}$

$I (θ)$ is not constant.

Alternatively, when $θ$ is zero the path difference between wave originating from $S_{1}$ and that from $S_{2}$ will be zero.

This corresponds to a maxima.

Optics Question 848

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Optics Question 848

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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