A slit of width a is illuminated by light of wavelength λ . The...

The position of the $n^{th}$ minimum in a single slit diffraction pattern on a screen at distance $D$ is given by $y_n = \dfrac{n D \lambda}{a}$.

For the $1^{st}$ minimum, $n = 1$, so $y_1 = \dfrac{D \lambda}{a}$.

For the $3^{rd}$ minimum, $n = 3$, so $y_3 = \dfrac{3 D \lambda}{a}$.

The linear separation between the $1^{st}$ and $3^{rd}$ minima on the same side of the central maximum is $\Delta y = y_3 - y_1$.

$\Delta y = \dfrac{3 D \lambda}{a} - \dfrac{D \lambda}{a} = 2\dfrac{D \lambda}{a}$.

Answer: $2\dfrac{D\lambda}{a}$