Two coherent narrow slits illuminate a distant screen. Keeping the slit separation d and the slit–to–screen distance D fixed, a student wishes to understand how the locations of bright and dark fringes arise and how they would be affected by changes in wavelength.
(i) Explain, with reasons based on path difference, why certain points on the screen appear bright while others appear dark.
(ii) Show algebraically that the linear distance between two successive bright fringes is the same everywhere on the screen under the small-angle approximation.
(iii) If the wavelength of light is doubled while d and D remain unchanged, state with justification how the positions of (a) the central maximum and (b) the first dark fringe will be affected.