In Young's double slit experiment, the distance between the slits is 2 mm and the slits are 1 m away, from the screen. Two interference patterns can be obtained on the screen due to light of wavelength ' ₁ ' and ' ₂ ' respectively. The separation on the screen between the 3^ rd order bright fringes on the two interference patterns is ( ₂=1 5 ₁ )

Step-by-step solution

Position of the n th order bright fringe: y_n = n D d . Given ₂ = 1.5 ₁ , the positions for n = 3 are: y_ 3,1 = 3 ₁ D d , y_ 3,2 = 3(1.5 ₁) D d = 4.5 ₁ D d . The separation is y = y_ 3,2 - y_ 3,1 = (4.5 - 3) ₁ D d = 1.5 ₁ D d . Substituting D = 1 m and d = 2 10⁻³ m , y = 1.5 1 2 10⁻³ ₁ = (0.75 10⁺³) ₁ . The result corresponds to option A .