Two wavelengths $\lambda_{1}$ and $\lambda_{2}$ are used in Young's double slit experiment $\lambda_{1}=450 \mathrm{~nm}$ and $\lambda_{2}=650 \mathrm{~nm}$. The minimum order of fringe produced by $\lambda_{2}$ which overlaps with the fringe produced by $\lambda_{1}$ is $n$. The value of $n$ is ______.

JEE Main · 2024 · 04 Apr 2024 · Shift 1 · Wave Optics

Two wavelengths

λ_{1}

and

λ_{2}

are used in Young's double slit experiment

λ_{1} = 450 nm

and

λ_{2} = 650 nm

. The minimum order of fringe produced by

λ_{2}

which overlaps with the fringe produced by

λ_{1}

n

. The value of

n

is ______.

Answer: 9

Solution

Fringes overlap when their positions coincide:

n_{2} λ_{2} = n_{1} λ_{1}

\frac{n _{2}}{n _{1}} = \frac{λ _{1}}{λ _{2}} = \frac{450}{650} = \frac{9}{13} .

The smallest integers are

n_{2} = 9

n_{1} = 13

. The minimum order of

λ_{2}

9

.
Answer: 9.

JEE Main · 2024 · 04 Apr 2024 · Shift 1 · Integer answer

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