Wave Optics

JEE Main level, single correct, medium

76 of 191

Question 76 of 191

Using Young's double slit experiment, a monochromatic light of wavelength 5000Å5000Å produces fringes of fringe width 0.5mm0.5mm. If another monochromatic light of wavelength 6000Å6000Å is used and the separation between the slits is doubled, then the new fringe width will be

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Answer: (D) 0.3mm0.3mm

We know that fringe width is given by, β=λDd\beta =\dfrac{\lambda D}{d}
⇒β′β=λ′λ×dd′=60005000×d2d\Rightarrow \dfrac{{\beta }^{'}}{\beta }=\dfrac{{\lambda }^{'}}{\lambda }\times \dfrac{d}{{d}^{'}}=\dfrac{6000}{5000}\times \dfrac{d}{2d}
⇒β′=65×2×0.5\Rightarrow {\beta }^{'}=\dfrac{6}{5\times 2}\times 0.5=0.3mm=0.3mm

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