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Q.

Sodium light of wavelengths $650 nm$ and $655 nm$ is used to study diffraction at a single slit of aperture $0.5 mm$ . The distance between the slit and the screen is $2.0 m$ . The separation between the positions of the first maxima of diffraction pattern obtained in the two cases is $____\times 10^{- 5} m$ .

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answer is 3.

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Detailed Solution

$\begin{aligned} a \sin θ = \frac{3 λ}{2} \\ \frac{y}{L} = θ = \frac{3 λ}{2 a} \\ y_{1} = \frac{3 λ_{1} L}{2 a} \\ y_{2} = \frac{3 λ_{2} L}{2 a} \end{aligned} \begin{aligned} L = 2 m \\ λ_{2} = 655 nm \\ λ_{1} = 650 nm \\ a = 0.5 nm \end{aligned} \begin{aligned} Δy = y_{2} - y_{1} = \frac{3 (λ_{2} - λ_{1})}{2 a} L \\ = \frac{3 (655 - 650)}{2 \times 0.5 \times 10^{- 3}} \times 2 \times 10^{- 9} \\ = \frac{3 \times 5 \times 2}{1 \times 10^{- 3}} \times 10^{- 9} \\ = 3 \times 10^{- 5} \end{aligned}$

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Sodium light of wavelengths 650 nm and 655 nm is used to study diffraction at a single slit of aperture 0.5 mm. The distance between the slit and the screen is 2.0 m. The separation between the positions of the first maxima of diffraction pattern obtained in the two cases is ____×10-5 m.