Light consisting of a plane waves of wavelength, ₁=8 10⁻⁵ ~cm and ₂=6 10⁻⁵ ~cm generates an interference pattern in Young's double slit experiment. If n₁ denotes the n₁ th dark fringe due to light of wavelength ₁ which coincides with n₂ th bright fringe due to light of wavelength ₂ , then

Step-by-step solution

Given, ₁=8 10⁻⁵ ~cm and ₂=6 10⁻⁵ ~cm Position n^ h , dark fringe (due to light of wavelength ₁ ) is given by, x_ n₁ = (2 n₁ 1 ) D ₁ 2 d Position of n₂ ^ th bright fringe due to light of wavelength ₂ is given by x_ n₂ = n₂ D ₂ d Since both the fringes are coincide to each other. Hence, aligned (2 n₁+1 ) D ₁ 2 d & = n₂ D ₂ d 2 n₁+1 n₂ & = 2 ₂ ₁ = 2 6 10⁻⁵ 8 10⁻⁵ 2 n₁+1 n₂ & = 3 2 4 n₁+2 & =3 n₂ 4 n₁-3 n₂ & =-2 4 n₁-3 n₂ & =-2 aligned when n₁=1 and n₂=2 , then Eq. (i) is satisfied. Hence, for n₁=1 and n₂=2 , given fri