A thin layer of liquid of an index of refraction, n = 1.334 is spread on a thin

Question

A thin layer of liquid of an index of refraction, n = 1.334 is spread on a thin transparent slide of n = 1.16 (figure below). Consider a light ray incident on the top surface of the slide Refer to the figure below and show on it. where ever relevant, all phase changes encountered by the incident ray due to reflection and / or transmission at and through all boundaries encountered bv the rav. For what minimum thickness, t, of the film will green light of wavelength 550.0 nm be of minimum reflection? If more oil is slowly added to the glass while light continues to hit its surface, what would be the film thickness for which a person spelling the oil and looking directly at that surface would then see the first bright light?

Explanation / Answer

the refractive idex of the two levels are = 1.334 [liquid]

n= 1.16 [slide]

so the change in phase occurs wherever the light has a transitiuon from a region of refractive index low to high

so the first occurs at the air and slide interface

second is from the slide and liquid interface

2] the thickness t of the film for minimum reflection = 2[refractive index]* t = nlamda

for minimum reflection n =1

so 2* 1.16* t = 1* 550

= t= 237.nm

3] 2[mue ]* t = [n+0.5]lamda

= n=0

so the value of t becomes

t= 118 nm

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