Wave Optics

JEE Main level, numerical answer, medium

36 of 191

Question 36 of 191

In two separate Young's double-slit experimental set-ups and two monochromatic light sources of different wavelengths are used to get fringes of equal width. The ratios of the slits separations and that of the wavelengths of light used are 2:12: 1 and 1:21: 2 respectively. The corresponding ratio of the distances between the slits and the respective screens (D1/D2D_{1} / D_{2}) is ____\_\_\_\_.

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Answer: 4

Fringe width in double slit: β=λDd\beta = \frac{\lambda D}{d}
Given:
d1d2=2:1\frac{d_1}{d_2} = 2:1 and λ1λ2=1:2\frac{\lambda_1}{\lambda_2} = 1:2, with equal fringe widths
For equal fringe widths:
λ1D1d1=λ2D2d2\frac{\lambda_1 D_1}{d_1} = \frac{\lambda_2 D_2}{d_2}
λ1λ2×D1D2=d1d2\frac{\lambda_1}{\lambda_2} \times \frac{D_1}{D_2} = \frac{d_1}{d_2}
12×D1D2=2\frac{1}{2} \times \frac{D_1}{D_2} = 2
D1D2=4\frac{D_1}{D_2} = 4

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