13. In Young’s double slit experiment, the slits are 2 mm apart and are illuminated by photons of two wavelengths $λ_1$ = 12000Å and $λ_2$ = 10000Å. At what minimum distance from the common central bright fringe on the screen 2 m from the slit will a bright fringe from one interference pattern coincide with a bright fringe from the other ?

13. In Young’s double slit experiment, the slits are 2 mm apart and are illuminated by photons of two wavelengths $λ_1$ = 12000Å and $λ_2$ = 10000Å. At what minimum distance from the common central bright fringe on the screen 2 m from the slit will a bright fringe from one interference pattern coincide with a bright fringe from the other ?

(a) 6 mm 

(b) 4 mm 

(c) 3 mm 

(d) 8 mm

Answer :  (a) 6 mm 

\( \frac{n \lambda_1 D}{d} = \frac{m \lambda_2 D}{d} \)

\( n \, 12000 \,\text{Å} = m \, 10000 \,\text{Å} \)

\( \frac{n}{m} = \frac{10}{12} = \frac{5}{6} \)

\( \frac{5 \times (12000 \,\text{Å}) \times 2}{2 \times 10^{-3}} = 60 \times 10^{-4} = 6 \times 10^{-3} = 0.6 \,\text{mm} \)