A student has a single slit that is 0.15 mm wide, cut in a thin metal foil…

A student has a single slit that is $0.15$ mm wide, cut in a thin metal foil. She lights it with an orange lamp of wavelength $600$ nm in air and looks at the pattern on a screen that is $1.20$ m behind the slit. First she measures the width of the central bright band in air. Then she sinks the slit and the screen together in a tank of water of refractive index $1.33$ and measures again. She keeps the lamp and the foil in the same positions the whole time, so only the surroundings of the slit change. She also reads that a beam keeps its width up to a certain distance from a slit, and she wants to know that distance. Find the width of the central maximum in air. Find the new width in water. Find the width of slit that, in water, gives back the width that was seen in air. Find also the Fresnel distance of the original slit in air.