In a two slit experiment with monochromatic light fringes are obtained on a screen placed at some distance from the sits. If the screen is moved by 5 × 10^-2 m towards the slits, the change in fringe width is 3 × 10^-5 m. If separation between the slits is 10^-3 m, the wavelength of light used is

6000 Å

$\beta=\frac{\lambda D}{d} \Rightarrow \beta \propto D$

$\Rightarrow \frac{\beta_1}{\beta_2}=\frac{D_1}{D_2} \Rightarrow \frac{\beta_1-\beta_2}{\beta_2}=\frac{D_1-D_2}{D_2} \Rightarrow \frac{\Delta \beta}{\Delta D}=\frac{\beta_2}{D_2}=\frac{\lambda_2}{d_2}$

$=\lambda_2=\frac{3 \times 10^{-5}}{5 \times 10^{-2}} \times 10^{-3}=6 \times 10^{-7}$ m = 6000 Å