યંગના પ્રયોગમાં બે સ્લિટ વચ્ચેનું અંતર \(0.5\, mm\) અને સ્લિટ અને પડદા વચ્ચેનું અંતર \(0.5\, m\) છે,\(5890\, A^o\) તરંગલંબાઈ ધરાવતા પ્રકાશ વાપરતા પ્રથમ અને ત્રીજી પ્રકાશિત શલાકા વચ્ચેનું અંતર શોધો.

A \(1178 \times 10^{-9} \,m\)
B \(1178 \times 10^{-6}\,m\)
C \(1178 \times 10^{-12} \,m\)
D \(5890 \times 10^{-7} \,m\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(1178 \times 10^{-6}\,m\)

Step-by-step Solution

Detailed explanation

\(\beta=\frac{\lambda D}{d}=\frac{5890 \times 10^{-10} \times 0.5}{0.5 \times 10^{-3}}\) \(=589 \times 10^{-6} m\) Distance between first and third bright fringe is \(2 \beta=2 \times 589 \times 10^{-6} m\) \(=1178 \times 10^{-6} m\)

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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