In two separate Young's double-slit experimental set-ups, two monochromatic light sources of different wavelengths are used to get fringes of equal width. The ratios of the slit separations and that of the wavelengths of light used are \(2: 1\) and \(1: 2\) respectively. The corresponding ratio of the distances between the slits and the respective screens ( \(D_1 / D_2\) ) is ___________ .

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(C) 4

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\(\beta_1=\beta_2\)
\(\frac{ D _1 \lambda_1}{d_1}=\frac{ D _2 \lambda_2}{d_2}\)
\(\frac{ D _1}{ D _2}=\frac{\lambda_2}{\lambda_1}\left(\frac{d_1}{d_2}\right)\)
\(=2 \times 2\)
\(\frac{ D _1}{ D _2}=4\)

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