The wavelength of light 500 nm is used in a Young's double slit experiment. The distance between the slits and screen is 100 cm and the slits are separated by 1 mm . Then find distance between fifth ( \(5^{\text {th }}\) ) and third ( \(3^{\text {rd }}\) ) bright fringes.

A 3 mn
B 2 mm
C 1 mm
D 4 mm

Verified Solution

Answer & Solution

Correct Answer

(C) 1 mm

Step-by-step Solution

Detailed explanation

(C) 1nm
distance between fringes
\(=\frac{5 \lambda \mathrm{D}}{d}-\frac{3 \lambda \mathrm{D}}{d}=\frac{2 \lambda \mathrm{D}}{d}\)
\(=\frac{2 \times 5 \times 10^{-7} \times 1}{1 \times 10^{-3}}\)
\(=10^{-3} \mathrm{~m}\)
\(=1 \mathrm{~mm}\)

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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