યંગના પ્રયોગમાં \(t\) જાડાઈની અને \(\mu\) વક્રીભવનાંક ધરાવતી પારદર્શક તકતી એક સ્લીટના માર્ગમાં મૂકવાથી મધ્યમાન પ્રકાશિત શલાકાનું \(n\) શલાકાની જાડાઈ જેટલું સ્થાનાંતર થાય છે.વપરાયેલ પ્રકાશની તરંગલંબાઈ \(\lambda\) હોય તો તકતીની જાડાઈ \(t\) કેટલી હશે?

A \(\frac{{2nD\lambda }}{{a\left( {\mu - 1} \right)}}\)
B \(\frac{{nD\lambda }}{{a\left( {\mu - 1} \right)}}\)
C \(\frac{{2D\lambda }}{{a\left( {\mu - 1} \right)}}\)
D \(\frac{{n\lambda }}{{\left( {\mu - 1} \right)}}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{{n\lambda }}{{\left( {\mu - 1} \right)}}\)

Step-by-step Solution

Detailed explanation

Path difference at central maxima \(\Delta x=(\mu-1)\, t,\) whole pattern will shift by same amount which will be given by \((\mu-1) \,t \frac{D}{d}=n \frac{\lambda D}{d},\) according to eh question \(t=\frac{n \lambda}{(\mu-1)}\) No option is matching, therefore question should…

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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