Your research teams uses interference to determine the thickness of a thin film such as guanine (index of refraction 1.80) that give fish scales their sheen. The apparatus used to determine the film's thickness has 2 slits 1.0 mm apart, a 600 nm laser light source, and a lens system to assure that parallel rays hit the slits. A screen is placed 1.0 meter away from the slits. Initially, you measure the interference pattern from the 2 slits on the screen. You then place the guanine film directly behind one of the slits and observe that the position of the central maximum of the screen shifts to the position formerly occupied by the 30th bright fringe from the central maximum.

Before the guanine film is placed behind one of the slits,

a) what is the difference in the distances (path lengths) that the light waves from the 2 slits travel to form the central maximum? to form the 30th fringe? express your answer in terms of the wavelength of the laser light.

b) Determine the distance from the central maximum to the 30th bright fringe as measured on the screen.

After the guanine film is placed behind one of the slits,

c) what must be the difference in the number of wavelengths from the slits to the screen for the light waves to form the new central maximum?

d) Determine the thickness of the guanine film.