\(6000 \times 10^{-8}\; \mathrm{cm}\) તરંગલંબાઈ ધરાવતો દ્રશ્ય પ્રકાશ એક સ્લીટ પર પડે છે જે શલાકા ઉત્પન્ન કરે છે. દ્વિતીય ન્યૂનતમ મધ્યસ્થ અધિકતમથી \(60^{\circ}\) એ જોવા મળે છે.જો પ્રથમ ન્યૂનતમ \(\theta_{1}\) ખૂણે જોવા મળતો હોય તો \(\theta_{1}\) કેટલા ......\(^o\) હશે?

A \(20\)
B \(45\)
C \(30\)
D \(25\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(25\)

Step-by-step Solution

Detailed explanation

\(\sin \theta=\frac{2 \lambda}{\omega}\) \(\sin 60^{\circ}=\frac{2 \lambda}{\omega}\) \(\sin \theta_{1}=\frac{\lambda}{\omega}=\frac{\sqrt{3}}{4}\) \(\theta_{1}=25^{\circ}\)

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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