આકૃતિમાં દર્શાવ્યા પ્રમાણે ઉદગમ \(S\) માંથી નિકળતા બે કિરણના સંપાતિકરણથી બિંદુ \(P\) આગળ વ્યતિકરણની ભાત જોવા મળે છે. તો બિંદુ \(P\) આગળ મળતી મહત્તમ તીવ્રતા \(I\) નું મૂલ્ય કેટલું હશે? (\(R\) એ સંપૂર્ણ પરાવર્તિક સપાટી છે)

A \(I\, = \,\frac{{2n\lambda }}{{\sqrt 3 - 1}}\)
B \(I\, = \,\frac{{(2n - 1)\lambda }}{{2(\sqrt 3 - 1)}}\)
C \(I\, = \,\frac{{(2n - 1\,\lambda )\sqrt 3 }}{{4(2 - \sqrt 3 )}}\)
D \(I\, = \,\frac{{(2n - 1)\lambda }}{{\sqrt 3 - 1}}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(I\, = \,\frac{{(2n - 1\,\lambda )\sqrt 3 }}{{4(2 - \sqrt 3 )}}\)

Step-by-step Solution

Detailed explanation

From the figure straight path \(\mathrm{SP}=2 l\) Reflected path \(\mathrm{SP}=2 l\) sec \(30^{\circ}\) So path difference is \(2 l\left(\sec 30^{\circ}-1\right)\) Also the ray, when reflected by the mirror, suffers a phase change of \(\pi\) So the total difference in phase is…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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