MHT CET · Physics · Wave Optics

Two sources of light \(0.6 \mathrm{~mm}\) apart and screen is placed at a distance of \(1.2 \mathrm{~m}\) from them. A light of wavelength \(6000 Å\) used. Then the phase difference between the two light waves interfering on the screen at a point at a distance \(3 \mathrm{~mm}\) from central bright band is

A \(6 \pi\) radian
B \(3 \pi\) radian
C \(4 \pi\) radian
D \(5 \pi\) radian

Verified Solution

Answer & Solution

Correct Answer

(D) \(5 \pi\) radian

Step-by-step Solution

Detailed explanation

Fringe width, \(W=\frac{\lambda . D}{d}=\frac{6000 \times 10^{-10} \times 1.2}{0.6 \times 10^{-3}}=1.2 \mathrm{~mm}\)
\(\therefore \quad\) Number of fringes (n) \(=\frac{3}{1.2}=2.5\)
\(\therefore \quad\) Phase difference,
\(\Delta \phi=2 \mathrm{n} \pi=2 \times 2.5 \pi=5 \pi\)

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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