AP Free Response Question 2010 Form B - B5

In a double-slit interference experiment, a parallel beam of monochromatic light is needed to illuminate two narrow parallel slits of width w that are a distance b apart in an opaque card as shown in the figure above. A lens is inserted between the point light source S and the slits in order to produce the parallel beam of light. The interference pattern is formed on a screen a distance D from the slits, where D >> b.

 (a) On the figure above, draw the lens at the appropriate place to produce the parallel beam of light, and label the location of the source relative to the lens with the appropriate optical parameter of the lens.

 (b) Draw two light rays from the source to the slits to show the production of the parallel rays.

 (c) In the interference pattern on the screen, the distance from the central bright fringe to the third bright fringe on one side is measured to be y3. Derive an expression for the wavelength of the light in terms of the given quantities and fundamental constants.

 (d) If the space between the slits and the screen was filled with a material having an index of refraction n > 1, would the distance between the bright fringes increase, decrease, or remain the same?     Explain your reasoning.