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

Question

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

TestHub · Accepted Answer

The condition for maxima in diffraction is,

$b \sin θ = (2 n + 1) \frac{λ}{2}$ .

For the first maxima $n = 1$ . Therefore,

$b \sin θ = \frac{3 λ}{2} \Rightarrow \sin θ = \frac{3 λ}{2 b} = \frac{y}{D} y = \frac{3 λ D}{2 b}$

Now the difference between the positions of the maxima will be,

$y_{1} - y_{2} = \frac{3 D}{2 b} (λ_{1} - λ_{2}) \Rightarrow y_{1} - y_{2} = \frac{3 \times 2}{2 \times 5 \times 10^{- 4}} \times (655 - 650) \times 10^{- 9} = 3 \times 10^{- 5} m$

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