In a Young's double-slit experiment, the two slits are kept 2 mm apart and the screen is positioned 140 cm away from the plane of the slits. The slits are illuminated with light of wavelength 600 nm. Find the distance of the third bright fringe, from the central maximum, in the interference pattern obtained on the screen.
If the wavelength of the incident light were changed to 480 nm, find out the shift in the position of third bright fringe from the central maximum. 
If the wavelength of the incident light were changed to 480 nm, find out the shift in the position of third bright fringe from the central maximum.  

We have Young's double slit experiment. 
Distance between the slits, d = 2 mm = 2 × 10^-3 m
Distance between the slit and the screen, D = 140 cm = 1.40 m
Wavelength of the monochromatic source of light, λ = 600 nm = 600 × 10^-9m = 6 × 10^-7
m
Position of bright fringes is given by, 

              $\boxed{{\mathrm{x}}_n = \mathrm{n\lambda }\frac{\mathrm{D}}{\mathrm{d}}}$ 

Here, we are considering the third fringe.

∴ Distance of the third bright fringe is, 
           ${\mathrm{x}}_3 = 3\mathrm{\lambda }\frac{\mathrm{D}}{\mathrm{d}}$
$\Rightarrow$       ${\mathrm{x}}_3 = 3\times 6\times {10}^{-7}\times \frac{1.40}{2 \times {10}^{-3}}$
               $$\begin{gathered} = 12.6 \times {10}^{-4} \\ = 1.26 \times {10}^{-3} \mathrm{m} \\ = 1.26 \mathrm{mm} \end{gathered}$$  

If the wavelength of incident light is changed to 480 nm, then
 $\mathrm{\lambda } = 480 \mathrm{nm} = 480 \times {10}^{-9} = 4.8 \times {10}^{-7}\mathrm{m}$ 

Distance of the third bright fringe is

            $$\begin{gathered} {\mathrm{x}}_3 = 3\mathrm{\lambda }\frac{\mathrm{D}}{\mathrm{d}} \\ = 3 \times 4.8 \times {10}^{-7} \times \frac{1.40}{2 \times {10}^{-3}} \\ = 10.08 \times {10}^{-4} \\ = 1.008 \times {10}^{-3}\mathrm{m} \\ = 1.01 \times {10}^{-3}\mathrm{m} \\ = 1.01 \mathrm{mm}. \end{gathered}$$ 

$\therefore$ Shift in the position of third bright fringe when there is a change in wavelngth,
        $= 1.26 - 1.01 = 0.25 \mathrm{mm}.$