MHT CET · Physics · Wave Optics

A single slit diffraction pattern is formed with white light. For what wavelength of light, the \(3^{\text {rd }}\) secondary maximum in diffraction pattern coincides with the \(2^{\text {nd }}\) secondary maximum in the pattern of red light of wavelength \(6000 Å\) ?

A \(4300 Å\)
B \(3500 Å\)
C \(4000 Å\)
D \(5000 Å\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(4300 Å\)

Step-by-step Solution

Detailed explanation

\(\begin{aligned} & \text { Distance of nth maximum } \mathrm{y}_{\mathrm{n}}=\left(\mathrm{n}+\frac{1}{2}\right) \frac{\lambda \mathrm{D}}{\mathrm{a}} \\ & \therefore \mathrm{y}_2=\left(2+\frac{1}{2}\right) \frac{\lambda_1 \mathrm{D}}{\mathrm{a}} \text { and } \mathrm{y}_3=\left(3+\frac{1}{2}\right) \frac{\lambda_2 \mathrm{D}}{\mathrm{a}} \\ & \therefore 2.5 \lambda_1=3.5 \lambda_2 \\ & \therefore 2.5 \times 6000=3.5 \lambda_2 \\ & \therefore \lambda_2=\frac{2.5 \times 6000}{3.5} \simeq 4300 A\end{aligned}\)

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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