SATHEE: Optics Question 472

Optics Question 472

Question: In Young’s double slit experiment, one of the slit is wider than other, so that amplitude of the light from one slit is double of that from other slit. If $I_{m}$ be the maximum intensity, the resultant intensity $I$ when they interfere at phase difference $ϕ$ is given by

Options:

A) $\frac{I_{m}}{9} (4 + 5 c o s ϕ)$

B) $\frac{I_{m}}{3} (1 + 2 c o s^{2} \frac{ϕ}{2})$

C) $\frac{I_{m}}{5} (1 + 4 c o s^{2} \frac{ϕ}{2})$

D) $\frac{I_{m}}{9} (1 + 8 c o s^{2} \frac{ϕ}{2})$

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Answer:

Correct Answer: D

Solution:

[d] It is given, $A_{2} = 2 A_{1}$

We know, intensity $\propto {(A m p l i t u d e)}^{2}$

Hence $\frac{I_{2}}{I_{1}} = {(\frac{A_{2}}{A_{1}})}^{2} = {(\frac{2 A_{1}}{A_{1}})}^{2} = 4$

$\Rightarrow I_{2} = 4 I_{1}$

Maximum intensity, $I_{m} = {(\sqrt{I_{1}} + \sqrt{I_{2}})}^{2}$

$= {(\sqrt{I_{1}} + \sqrt{4 I_{1}})}^{2} = {(3 \sqrt{I_{1}})}^{2} = 9 I_{1}$

Hence $I_{1} = \frac{I_{m}}{9}$

Resultant intensity, $I = I_{1} + I_{2} + 2 \sqrt{I_{1} I_{2}} \cos ϕ$

$= I_{1} + 4 I_{1} + 2 \sqrt{I_{1} (4 I_{1})} \cos ϕ$

$= 5 I_{1} + 4 I_{1} \cos ϕ = I_{1} + 4 I_{1} + 4 I_{1} \cos ϕ$

$= I_{1} + 4 I_{1} (1 + c o s ϕ)$

$= I_{1} + 8 I_{1} \cos^{2} ϕ$

$(∴ 1 + \cos ϕ = 2 \cos^{2} \frac{ϕ}{2})$

$I = \frac{I_{m}}{9} (1 + 8 c s o^{2} \frac{ϕ}{2})$ Putting the value of $I_{1}$ from eqn. (i), we get $I = \frac{I_{m}}{9} (1 + 8 \cos^{2} \frac{ϕ}{2})$

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Optics Question 472

Question: In Young’s double slit experiment, one of the slit is wider than other, so that amplitude of the light from one slit is double of that from other slit. If $I_{m}$ be the maximum intensity, the resultant intensity $I$ when they interfere at phase difference $ϕ$ is given by

Options:

Answer:

Solution:

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Optics Question 472

Question: In Young’s double slit experiment, one of the slit is wider than other, so that amplitude of the light from one slit is double of that from other slit. If Im be the maximum intensity, the resultant intensity I when they interfere at phase difference ϕ is given by

Options:

Answer:

Solution:

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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Question: In Young’s double slit experiment, one of the slit is wider than other, so that amplitude of the light from one slit is double of that from other slit. If $I_{m}$ be the maximum intensity, the resultant intensity $I$ when they interfere at phase difference $ϕ$ is given by