Working on your car, you spill oil (index of refraction = 1.55) on the ground in

Question

Working on your car, you spill oil

(index of refraction = 1.55)

on the ground into a puddle of water

(n = 1.33).

You notice a rainbow pattern appear across the oil slick. Recalling the lessons you learned in physics class, you realize that you can calculate where constructive and destructive interference occur based on the thickness of the oil slick. (Assume that the average wavelength is 526 nm.)

(a) What are the first three thicknesses necessary for constructive interference? (Enter your answers from smallest to largest.)

(b) What are the first three (nonzero) thicknesses necessary for destructive interference? (Enter your answers from smallest to largest.)

nm nm nm Working on your car, you spill oil (index of refraction = 1.55) on the ground into a puddle of water (n = 1.33). You notice a rainbow pattern appear across the oil slick. Recalling the lessons you learned in physics class, you realize that you can calculate where constructive and destructive interference occur based on the thickness of the oil slick. (Assume that the average wavelength is 526 nm.) a) What are the first three thicknesses necessary for constructive interference? (Enter your answers from smallest to largest.) (b) What are the first three (nonzero) thicknesses necessary for destructive interference? (Enter your answers from smallest to largest.)

Explanation / Answer

one low to high

a) so consuctive

(m +1/2) lambda/n = 2 d

d = ( m + 1/2) lambda/(2n)

so first = 1/2*500/(2*1.55)= 80.65 nm

second = 3/2*500/(2*1.55)=241.94 nm

third = 5/2*500/(2*1.55)= 403.23 nm

b) destructive when

m lambda/n = 2 d

d = m lambda/2n

so first = 1*500/(2*1.55)=161.3 nm

second = 2*500/(2*1.55)=322.6 nm

third = 493.9 nm

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