COMEDK · Physics · 26. Wave Optics

In a Young's double slit experiment, the slit separation is 1.5 mm. The setup is illuminated simultaneously by light of wavelengths 6000 Å and 8000 Å. The screen is placed at a distance of 1.5 m from the slits. It is observed that at a certain point P on the screen which is 4.8mm from the central maximum, fringes due to both the wavelengths coincide. Which of the following options are correct?

A Light of wavelength 6000 Å produces a dark fringe and light of wavelength 8000 Å produces a bright fringe at P
B Light of wavelength 6000 Å produces a bright fringe and light of wavelength 8000 Å produces a dark fringe at P
C Light of wavelength 6000 Å and light of wavelength 8000 Å both produce a dark fringe at P
D Light of wavelength 6000 Å and light of wavelength 8000 Å both produce a bright fringe at P

Verified Solution

Answer & Solution

Correct Answer

(D) Light of wavelength 6000 Å and light of wavelength 8000 Å both produce a bright fringe at P

Step-by-step Solution

Detailed explanation

The path difference at point P is given by \(\Delta x = \dfrac{y d}{D}\). Substituting the given values: \(\Delta x = \dfrac{4.8 \times 10^{-3} \times 1.5 \times 10^{-3}}{1.5} = 4.8 \times 10^{-6}\) m. For wavelength \(\lambda_1 = 6000 \times 10^{-10}\) m \(= 6 \times 10^{-7}\)…

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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