યંગના બે સ્લિટના પ્રયોગમાં સ્લિટને એક બીજાથી \(0.320\,mm\) દૂર રાખવામાં આવે છે. આ સ્લિટ્સ પર \(\lambda=500\, nm\) ની તરંગલંબાઇનો પ્રકાશ આપાત થાય છે. \( - {30^o} \le \theta \le {30^o}\) ની કોણીય અવધીમાં જોવા મળતી પ્રકાશિત શલાકાઓની કુલ સંખ્યા હશે કેટલી હશે?

A \(640\)
B \(320\)
C \(321\)
D \(641\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(641\)

Step-by-step Solution

Detailed explanation

\(\Delta X_{\max }=d \sin \theta=0.32 \sin 30=0.16\, \mathrm{mm}\) \(\therefore n = \frac{{\Delta {X_{\max }}}}{\lambda }\) \( = \frac{{0.16 \times {{10}^{ - 3}}}}{{500 \times {{10}^{ - 9}}}}\) \(=\frac{0.16 \times 10^{6}}{500}=\frac{1600}{5}=320\) Number of…

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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