Sodium light of wavelengths 650nm and 655nm is used to study...

The condition for maxima in diffraction is,

$bsin\theta = \left(2n + 1\right)\dfrac{\lambda}{2}$.

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

$bsin\theta = \dfrac{3\lambda}{2} ⇒ sin\theta = \dfrac{3\lambda}{2b} = \dfrac{y}{D}y = \dfrac{3\lambdaD}{2b}$

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

${y}_{1} - {y}_{2} = \dfrac{3D}{2b}\left({\lambda}_{1} - {\lambda}_{2}\right) ⇒ {y}_{1} - {y}_{2} = \dfrac{3 \times 2}{2 \times 5 \times {10}^{- 4}} \times \left(655 - 650\right) \times {10}^{- 9} = 3 \times {10}^{- 5}m$