Your research teams uses interference to determine the thickness of a thin film

Question

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.

Explanation / Answer

d = 1 mm

lambda = 600 nm

D = 1 m

Before the film is placed....

a)path difference = dx = n*lambda

For central maxima, n = 0

So, dx = 0....

For 30th bright fringe,

n = 30

So, dx = 30*600 nm = 18000 nm = 1.8*10^-5 m

b) distace , y = n * D * lambda / d = 30 * 1 * 600*10^-9 / 0.001 = 0.018 m

After the film is placed

c) the path difference increases by dx' = ut,

where u =refractive index of film

and t = thickness

Here it is said that thethe position of the central maximum of the screen shifts to the position formerly occupied by the 30th bright fringe from the central maximum...

So, difference must be 30 wavelengths

d) Also, for central maximum, path difference must be ZERO

this is possible only if dx + dx' = 0

But dx = 1.8*10^-5 m...since it is at the postition of 30th maxima

So, dx' = dx

So, 1.8*10^-5 = 1.8 * t

SO, t = 10^-5 m

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