Monochromatic light passes through a double-slit arrangement and produces an interference pattern on a screen 2.0m away. The center-to-center separation of the slits is 0.25mm. Experimental measurement shows that the third-order bright fringe (counting the central maximum as order 0) appears 6.0cm above the central maximum on the screen.
(a) Derive an expression for the vertical position ym of the mth bright fringe on the screen in terms of the slit separation d, the wavelength λ, the distance L to the screen, and the integer m. Clearly state any approximations used.
(b) Using the result from part (a) and the measured data, calculate the wavelength of the light.
(c) Determine the phase difference between the two waves arriving at the third-order bright fringe.
(d) Suppose the apparatus is modified so that the path length from one slit to the same point on the screen increases by 0.50λ. Predict quantitatively whether that point will now correspond to a maximum, a minimum, or an intermediate intensity, and explain.