MHT CET · Physics · Wave Optics

In Young's double slit experiment, the fifth maximum with wavelength ' \(\lambda_1\) ' is at a distance ' \(\mathrm{y}_1\) ' and the same maximum with wavelength ' \(\lambda_2\) ' is at a distance ' \(y_2\) ' measured from the central bright band. Then \(\frac{y_1}{y_2}\) is equal to [D and \(d\) are constant]

A \(\frac{\lambda_1}{\lambda_2}\)
B \(\frac{\lambda_2}{\lambda_1}\)
C \(\frac{\lambda_1^2}{\lambda_2^2}\)
D \(\frac{\lambda_2^2}{\lambda_1^2}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{\lambda_1}{\lambda_2}\)

Step-by-step Solution

Detailed explanation

The equations for the position of the fringe from the central maxima are given as
\(\begin{aligned}
\mathrm{y}_1 & =\frac{5 \lambda_1 \mathrm{D}}{\mathrm{d}} \\
\mathrm{y}_2 & =\frac{5 \lambda_2 \mathrm{D}}{\mathrm{d}} \\
\therefore \quad \frac{\mathrm{y}_1}{\mathrm{y}_2} & =\frac{\lambda_1}{\lambda_2}
\end{aligned}\)

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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