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JEE Main 2009

Exam: JEE Main
Year: 2009
Subject: Physics
Chapter: Wave Optics

JEE Main 2009 · Physics · Wave Optics

A mixture of light, consisting of wavelength 590 nm and an unknown...

A mixture of light, consisting of wavelength

590 \mathrm{ nm} and an unknown wavelength, illuminates Young's double slit and gives rise to two overlapping interference patterns on the screen. The central maximum of both lights coincide. Further, it is observed that the third bright fringe of known light coincides with the

4^{

\text{th }

}

bright fringe of the unknown light. From this data, the wavelength of the unknown light is

Options

A $393.4 \mathrm{~nm}$
B $885.0 \mathrm{~nm}$
C $442.5 \mathrm{~nm}$
D $776.8 \mathrm{~nm}$

Correct answer

C. $442.5 \mathrm{~nm}$

Step-by-step solution

\begin{aligned}& 3 \lambda_1=4 \lambda_2 \\ & \Rightarrow \lambda_2=\frac{3}{4} \lambda_1=\frac{3}{4} \times590=\frac{1770}{4}=442.5 \mathrm{~nm} \end{aligned}

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