A laboratory dish, 20 cm in diameter, is half filled with water. One at a time,

Question

A laboratory dish, 20 cm in diameter, is half filled with water. One at a time, 0.47 L drops of oil from a micropipette are dropped onto the surface of the water, where they spread out into a uniform thin film. After the first drop is added, the intensity of 610 nm light reflected from the surface is very low. As more drops are added, the reflected intensity increases, then decreases again to a minimum after a total of 13 drops have been added. Part A What is the index of refraction of the oil? Express your answer using two significant figures.

Explanation / Answer

volume of oildrop=0.47 uL= 0.47x10-6 L= 0.47x10-9 m3 .

radius= 20cm/2= 10 cm=0.1 m

let t= thickness of the oil film

pi r2 t= 0.47x10-9 .

3.14 (0.1)2 t= 0.47x10-9

t=1.497x10-8 m

phase drop because of one drop= 2nt where n= refractive index

for 13 drops phase differnce= 13 (2 nt)= 26 nt

after 13 drops, we have a minima. so 26nt= lambda

26(n)(1.497x10-8 )=610x10-9

n= 1.51

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