Wave Optics

JEE Main level, single correct, medium

116 of 191

Question 116 of 191

A mixture of light, consisting of wavelength 590 nm590 \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 4th 4^{\text {th }} bright fringe of the unknown light. From this data, the wavelength of the unknown light is

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Answer: (C) 442.5 nm442.5 \mathrm{~nm}

3λ1=4λ2⇒λ2=34λ1=34×590=17704=442.5 nm\begin{aligned} & 3 \lambda_1=4 \lambda_2 \\ & \Rightarrow \lambda_2=\frac{3}{4} \lambda_1=\frac{3}{4} \times 590=\frac{1770}{4}=442.5 \mathrm{~nm} \end{aligned}

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