SATHEE: Physics And Measurement Question 298

Physics And Measurement Question 298

Question: Intensity observed in an interference pattern is $I = I_{0} S i n^{2}$ . $A t θ = 30^{o}$ intensity $I = 5 \pm 0.0020 W / m^{2}$ . Find percentage error in angle if $I_{0} = 20 W / m^{2}$

Options:

A) $\frac{4}{π} \sqrt{3} \times 10^{- 2}$

B) $\frac{2}{π} \sqrt{3} \times 10^{- 2}$

C) $\frac{1}{π} \sqrt{3} \times 10^{- 2}$

D) $\frac{3}{π} \sqrt{3} \times 10^{- 2}$

Show Answer

Answer:

Correct Answer: A

Solution:

[a] $I = I_{0} \sin^{2} θ \Rightarrow θ = \sin^{- 1} \sqrt{\frac{I}{I_{0}}}$

$d θ = \frac{1}{2} \frac{\sqrt{I_{0}}}{\sqrt{I_{0} - I}} \frac{d I}{\sqrt{I_{0} \sqrt{I}}}$

$\frac{d θ}{θ} = \frac{1}{2} \frac{d I}{\sqrt{I (I_{0} - I)} \sin^{- 1} \sqrt{I / I_{0}}}$
$∴$

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