In young's double slit experiment, the slits are separated by 0.28 mm and the screen is placed 1.4 m away. The distance between the central bright fringe and the fourth bright fringe is measured to be 12 cm . Then the wavelength of light used in the experiment is __________ .

A 660 nm
B 550 nm
C 600 nm
D 500 nm

Verified Solution

Answer & Solution

Correct Answer

(C) 600 nm

Step-by-step Solution

Detailed explanation

(C) 600 nm
Slits separation \(d=0.28 \mathrm{~mm}\)
\(
\text { Screen } \begin{aligned}
\mathrm{D} & =1.4 \mathrm{~m} \\
n & =4^{\text {th }} \text { bright }
\end{aligned}
\)
Distance between the central bright fringe and the fourth bright fringe \(x=1.2 \mathrm{~cm}\)
For bright fringe path difference
\(\frac{x d}{\mathrm{D}}=n \lambda\)
\(\therefore \quad \lambda=\frac{x_{4} d}{n \mathrm{D}}\)
\(\therefore \lambda=\frac{1.2 \times 10^{-2} \times 0.28 \times 10^{-3}}{4 \times 1.4}\)
\(
\begin{aligned}
& \lambda=6 \times 10^{-7} \mathrm{~m} \\
& \lambda=600 \mathrm{~nm}
\end{aligned}
\)

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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