Sodium light of wavelengths 650 nm and 655 nm is used to study diffraction at a single slit of aperture 0.5mm. The distance between the slit and the screen is 2.0m. 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

$a \sin θ = \frac{3 λ}{2}$

$\begin{array}{l} \frac{y}{L} = θ = \frac{3 λ}{2 a} L = 2 m \\ y_{1} = \frac{3 λ_{1} L}{2 a} λ_{2} = 655 n m \\ y_{2} = \frac{3 λ_{2} L}{2 a} λ_{1} = 650 n m \\ a = 0.5 n m \\ Δ y = y_{2} - y_{1} = \frac{3 (λ_{2} - λ_{1})}{2 a} L \\ = \frac{3 (655 - 650)}{2 \times 0.5 \times 10^{- 3}} \times 2 \times 10^{- 9} \\ = \frac{3 \times 5 \times 2}{1 \times 10^{- 3}} \times 10^{- 9} = 3 \times 10^{- 5} \end{array}$