(896) Problem 13: Light of wavelength 426 nm in air undergoes constructive inter

Question

(896) Problem 13: Light of wavelength 426 nm in air undergoes constructive interference when it is perpendicularly reflected from an oil spill on a plastic sheet. The refractive index of the oil is 1.25 and that of the plastic is 14 G What is the nonzero thickness, in nanometers, of the thinnest oil film that causes such interference? cosO) tan acos) sinhO) sin cotan0 asin0 atan)acotan( 0 coshO tanh0 cotanh0 Degrees Radians END BACKSPACE DEL CLEAR Submit Hint I give up! Hints: 2% deduction per hint. Hints remaining: 4 Feedback: 2% deduction per feedback.

Explanation / Answer

13. lambda = 426 nm

refractive index, n = 1.25 ( oil)

refractive index plastic, n' = 1.4

let thickness of the oil film be t

the light undergoes a phase reversal at air - oil and oil - plastic interfacfes as n air < n oil and n oil < n plastic

hence

for constructive interference condition of destructive interference has to be used

so,

path difference = 2t*n = lambda/2

t = lambda/4n = 426/4*1.25 = 85.2 nm is the thickness of the thinnest oil film that will cause constructive interfercen on the plastic

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