Wave Optics

Two coherent sources S 1 a n d S 2 S_{1}~and~S_{2} separated by distance 2 λ 2 \lambda emit light of wavelength λ \lambda , in phase as shown. A circular wire of radius 100 λ 100 \lambda is placed in such a way that S 1 S 2 S_{1}S_{2} lies in its plane and the mid point of S 1 S 2 S_{1}S_{2} is at the centre of wire. The angular positions on the wire for which intensity reduces to half of its maximum value for the first time is given as θ \theta . Find the value of 32 c o s θ 32cos \theta


The answer is 4.00.

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1 solution

Vivek Modi
Apr 16, 2015

would have been much easier if the decimal places have had not been included in the answers...

awesome! I used law of cosines, but your solution is much more cool.

Claudio Felipe - 6 years ago

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Thanks...!!

Vivek Modi - 6 years ago

Does 'first time' indicate smallest value for theta? In that case the answer should be 28 not 4. We should take the phase difference as 7/4 l a m d a lamda and not 1/4 lamda. As at that time phase difference is closest to 2 lamda. Hence c o s θ cos \theta comes out to be 7/8

Adwait Godbole - 5 years, 10 months ago

i think this is wrong since we used pathdiff=dsin(theta) when D>>d which in this case is not

ARYAN GOYAT - 4 years, 7 months ago

infact cos(theta) come out to 0.0125 if we dont take approx and use cosine rule only so ans should be 0.4

ARYAN GOYAT - 4 years, 7 months ago

did the same!!!!

A Former Brilliant Member - 3 years, 7 months ago

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