A light source, which emits two wavelengths $λ_{1} = 400 nm and λ_{2} = 600 nm,$ is used in Young’s double site experiment. If recorded fringe widths for $λ_{1}$ and $λ_{2}$ are $β_{1}$ and $β_{2}$ and the number of fringes for them within a distance y on one side of the central maximum are $m_{1}$ and $m_{2}$ , respectively, then

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$β_{2} > β_{1}$

The angular separation of fringes of $λ_{1}$ is greater than $λ_{2}$

$m_{1} > m_{2}$

From the central maximum, $3^{rd}$ maximum of $λ_{2}$ overlaps with $5^{th}$ minimum of $λ_{1}$

answer is A, B, C.

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Detailed Solution

The figure width in Young’s double slit experiment is given by $β = λ D / d .$ Thus, the ratio of fringe width for the two wavelengths is $β_{1} / β_{2} = λ_{1} / λ_{2} = 400 / 600 = 2 / 3.$
Question Image
The number of fringes in a distance y are $m = y / β .$ Hence, the ratio of number of fringes of two wavelengths in a given distance y is
$m_{1} / m_{2} = β_{2} / β_{1} = 3 / 2.$
The third maximum for $λ_{2}$ and fifth minimum of $λ_{1}$ will occur at
$y_{2} = 3 β_{2} = 3 \times 600 D / d = 1800 D / d, y_{1} = (5 - 1 / 2) β_{1} = 4.5 \times 400 D / d = 1800 D / d .$