In a Young's double slit experiment, two different monochromatic light sources are used one after the other to form interference patterns on a screen. If the ratio of the wavelengths of the two light sources is 3 : 2 , what will be the ratio of the number of fringes observed in the exact same field of view on the screen?

Step-by-step solution

The fringe width in a Young's double slit experiment is given by = D d . The total width of a region containing n fringes is y = n = n D d . For a fixed region on the screen (constant y ), and with the same experimental setup (constant D and d ), the number of fringes is inversely proportional to the wavelength of the light used. Therefore, n 1 , which implies n₁ ₁ = n₂ ₂ . The ratio of the number of fringes is n₁ n₂ = ₂ ₁ . Given the wavelength ratio ₁ ₂ = 3 2 , the ratio of the number of fringes will be 2 3 , or