JEE Main 2026 — Jan 23, Shift 1 — Physics solution

JEE Main2026Jan 23, Shift 1Physics

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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Solution

Fringe width: $β = \frac{λ D}{d}$ . Equal fringe widths give:

$\frac{λ _{1} D _{1}}{d _{1}} = \frac{λ _{2} D _{2}}{d _{2}} \Rightarrow \frac{D _{1}}{D _{2}} = \frac{λ _{2}}{λ _{1}} \cdot \frac{d _{1}}{d _{2}}$

Given $d_{1} : d_{2} = 2 : 1$ and $λ_{1} : λ_{2} = 1 : 2$ , so $λ_{2} / λ_{1} = 2$ and $d_{1} / d_{2} = 2$ :

$\frac{D _{1}}{D _{2}} = 2 \times 2 = 4$

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