1. **Problem Statement:** We have a Young's double-slit experiment with slit separation $a$, distance to screen $D=2$ m, and a point $M$ on the screen located 5 mm from the central bright fringe where the 5th order fringe is observed. 2. **Formula Used:** The position of the $m^{th}$ bright fringe in Young's double-slit experiment is given by: $$y_m = m \frac{\lambda D}{a}$$ where: - $y_m$ is the fringe position from the central maximum, - $m$ is the fringe order (integer), - $\lambda$ is the wavelength of light, - $D$ is the distance from slits to screen, - $a$ is the slit separation. 3. **Given Data:** - $m = 5$ - $y_5 = 5$ mm = $5 \times 10^{-3}$ m - $D = 2$ m 4. **Calculate Wavelength $\lambda$:** Rearranging the formula: $$\lambda = \frac{y_m a}{m D}$$ 5. **Fringe Spacing $\Delta y$:** Fringe spacing is the distance between adjacent bright fringes: $$\Delta y = \frac{\lambda D}{a}$$ 6. **Effect of Changing Slit Spacing $a$:** - Increasing $a$ decreases fringe spacing $\Delta y$ (fringes get closer). - Decreasing $a$ increases fringe spacing $\Delta y$ (fringes spread out). 7. **Summary:** - The position of the 5th order fringe is $y_5 = 5$ mm. - Using the formula, $\lambda$ can be found if $a$ is known. - Fringe spacing depends inversely on slit separation $a$. **Final formula for fringe spacing:** $$\boxed{\Delta y = \frac{\lambda D}{a}}$$ **Note:** Without the value of $a$ or $\lambda$, numerical calculation is not possible here.